FACULTY OF SCIENCE AND TECHNOLOGY MASTER’S THESIS
Study programme/specialisation: Industrial Economics and Technology Management	Spring semester, 2020. Open
Author: Terje Berg
Programme coordinator: Supervisor(s): Harald Haukås
Title of master’s thesis: Quality Minus Junk – A Study Across 44 Countries
Credits: 30
Keywords: Empirical asset pricing, QMJ, Factor model, Quality factor	Number of pages: 44 + supplemental material/other: 52 Stavanger, 15.June 2020

Abstract

This thesis seeks to further investigate the quality factor which is reported in the research literature on financial market anomalies and related to systematic investment strategies. The research is done first by a literature study, then by examining whether the findings from Asness, Frazzini and Pedersen’s paper “quality minus junk” [1] can be replicated when increasing the dataset from 24 countries to 44. The quality factor is a proxy based on an asset pricing model where the future discounted payoffs is split into separate terms relating to profitability, growth and safety. I provide evidence confirming two research hypotheses, namely that 1: There is a positive and significant relationship between price and quality, and 2: an abnormal risk-adjusted return can be earned by investing in high-quality stocks and shorting low-quality stocks.

The first finding on the positive relationship between price and quality shows that the model specification based on modern asset pricing has explanatory power on stock prices, but most of the cross-sectional variation in prices is still unexplained. This finding is true in 40 out of the 44 countries examined for the sample data between 2005 and 2019.

The second finding shows that a factor-mimicking portfolio (QMJ) going long on the highest quality firms and shorting the low-quality stocks earns a significant risk-adjusted return with a Sharpe ratio after hedging for other factor exposures just above 1. The risk-adjusted alpha was positive for 43 out of the 44 countries in the sample.

This thesis contributes the empirical asset pricing field by confirming the results from Asness et al. using a broad sample of 44 countries obtained from a different data provider and with all the factors built from scratch. In their paper they conclude the abnormal risk-adjusted returns of quality stock are due to mispricing and they are unable to find a risk-based explanation. This study supports those conclusions and I find that quality deliver consistent returns during times of distress as well as in times of boom. It is difficult to find a risk-based explanation of the abnormal returns or a behavior-based story for why investors underweight high-quality stocks. Rather, the intelligent investor should add the QMJ factor to his or her toolbox of factors which can be used to create a portfolio aligned with the investor’s goals and preferences.

An investment operation is one which, upon thorough analysis, promises safety of principal and a satisfactory return. Operations not meeting these requirements are speculative.

–Benjamin Graham (1934)

Contents

Abstract. 1

1 Introduction.. 4

2 Background.. 5

2.1 A Brief History of Asset Pricing. 5

2.2 Modern Asset Pricing. 6

2.2.1 Consumption-Based Model 6

2.2.2 Expected Return-Beta Model 7

2.2.3 Selecting factors – market anomalies. 8

2.3 Quality as a Factor. 10

2.3.1 Overview.. 10

2.3.2 Model for Quality. 10

3 Data. 13

3.1 Quantopian Research Platform.. 13

3.2 Data Sources 13

3.3 Data Processing. 13

3.4 Summary Statistics. 14

4 Analysis. 16

4.1 Overview.. 16

4.2 Correlations Between Factor Components. 16

4.3 Regression Analysis. 20

4.4 Portfolio Forming. 22

4.5 The Price of Quality Stocks 23

4.5.1 Persistence of Quality. 23

4.5.2 Price of Quality in the Cross-Section. 25

4.6 The Return of Quality Stocks. 29

4.6.1 The Return of Univariate Portfolio Sorts on Quality. 29

4.6.2 The Return on the QMJ Factor 33

4.7 Time-varying Return of Quality. 37

4.8 Algorithmic Trading. 40

5 Conclusion.. 42

References. 43

Appendix 1 – Table A-1. 45

Appendix 2 – Table A-2. 50

Appendix 3 – Python notebook with code used to perform analysis. 64

List of Figures

Figure 2‑1: Relationship of Intrinsic value factors to market price. 6

Figure 4‑1: Quality plotted against its sub-factors profitability, growth and safety. 17

Figure 4‑2: Pair-plots of the profitability factor and its sub-components. 18

Figure 4‑3: Pair-plots of the growth factor and its sub-components. 19

Figure 4‑4: Pair-plots of the safety factor and its sub-components. 20

Figure 4‑5: Portfolio mean return versus cross-sectional regressions [23]. 22

Figure 4‑6: This chart shows the high-minus low of quality sorted portfolios 24

Figure 4‑7: Change in mean portfolio quality scores from time of formation. 24

Figure 4‑8: Typical scatterplot of time averaged sample data and fitted regression line. 25

Figure 4‑9: This chart’s left-hand axis shows the slope coefficient estimates for a regression of price on quality for each country. 27

Figure 4‑10: The chart shows market-weighted means of the countries with statistically significant difference portfolios for excess returns and 4-factor alphas. 31

Figure 4‑11: This chart shows the fama-french-carhart abnormal returns (alpha) for the regressions of the quality-sorted difference portfolio’s monthly excess return 32

Figure 4‑12: This chart shows the global market weight mean of the Sharpe ratios and the information ratios of quality-sorted portfolios 33

Figure 4‑13: QMJ 4-factor alpha information ratios. 35

Figure 4‑14: The chart shows the Global average cumulative excess returns from the factor portfolios. 38

Figure 4‑15: The time-varying price of quality. 38

Figure 4‑16: This chart shows the cumulative 4-factor alpha factor abnormal returns 39

Figure 4‑17: Abnormal returns (alpha) of the Quality sorted portfolios when adjusted for Fama-French-Carhart risk factors. 39

Figure 4‑18: Cumulative excess returns of a QMJ portfolio formed every month. 40

Figure 4‑19: Workflow for quantitative investment, adopted from [31] 41

List of Tables

Table 2‑1: Variable definitions. 12

Table 3‑1: Summary statistics of data sample. 14

Table 4‑1: Pearson product-moment correlations between quality and sub-factors. 16

Table 4‑2: The price of quality - Cross sectional regressions. 27

Table 4‑3: Return on Quality - excerpt from Table A-2 showing two countries of interest. 32

Table 4‑4: Regressions of QMJ returns on risk factors. 35

1 Introduction

The goal of this thesis is to examine factor models used in the asset pricing of stocks. More specifically, I wish to determine whether the findings relating to the quality factor proposed by Asness, Frazzini and Pedersen [1] can be replicated using an extensive data set from 44 countries, available through the novel Quantopian cloud platform. Quality is defined as “a characteristic that investors, all else held equal, should be willing to pay a higher price for”. The overarching question they ask is: “Do the highest quality firms command the highest prices?” They conclude that the quality factor presents a puzzle to asset pricing theory, because they are unable to explain the high returns of “quality firms” based on a risk story or to demonstrate that prices in the cross-section vary “enough” with quality measures.

This puzzle intrigued me to dig into the field of empirical asset pricing and learn the skills to put factor models to the test. In order to prove or disprove the findings from Asness et al. I have formulated these two hypotheses that need to be tested:

1) There is a positive, but weak, correlation between asset price and a firm’s quality.

2) A significant risk-adjusted return can be earned by investing in (going long) high-quality stocks and shorting the low-quality stocks.

2 Background

2.1 A Brief History of Asset Pricing

The problem of efficient allocation of limited resources is a fundamental issue to understand in economics. As student we are introduced to utility theory as model to understand how people use their resources efficiently by taking into account preferences, e.g. to risk or other factors. Utility theory is used to expand into the modern portfolio theory. Markowitz’s minimum variance problem and the capital asset pricing model (CAPM) are presented as frameworks to understand pricing of individual assets under market equilibrium. This framework works well as an academic model, but given its many unrealistic assumptions the traditional derivations do not hold up against empirical data [2]. Still, surveys show that more than 70% of companies use the simple CAPM for determining cost of capital [3] (and for which it may be good enough).

Since the CAPM was developed in the 1960s alternatives and improvements have been proposed by several researchers. Ross developed the alternative arbitrage pricing theory (APT) [4] and perhaps most notably Fama and French who published their three-factor model [5] (and revised it with a five-factor asset pricing model in 2015 [6]). This work has been of special interest for security analysts and investors who try to predict the future price movement of securities or take advantage of certain market behaviour.

The typical textbook economic theory teaches us that stock prices in the market fully reflect all available information, sometimes referred to as the efficient market hypothesis [7]. This should imply that new information quickly affects asset prices and that the current available information cannot be used to predict future returns. What investors with decades of practical experience teach us on the other hand is a more nuanced perspective. Benjamin Graham, both an academic and practitioner writes together with David Dodd in their landmark textbook from 1934, “Security analysis” [8]:

“The market is not a weighing machine, on which the value of each issue is recorded by an exact and impersonal mechanism, in accordance with its specific qualities. Rather should we say that the market is a voting machine, whereon countless individuals register choices which are the product partly of reason and partly of emotion.”

Graham & Dodd were also some of the first authors to break down factors that affect the market prices and in doing so they made a sharp distinction between what they called speculative factors and analytical (or investment) factors. The purpose of including Figure 2‑1 is to show that there is long timeline from those early “experience-based” observations of market factors to the more quantitative studies of recent years and attempts to explain them for instance by behavioural economics and factor models. Some of these explanations of how humans don’t act like the rational Homo Economicus, like prospect theory, have have been popularized through the book “Thinking, fast and slow” [9] and has won researchers like Kahneman and Vernon the Nobel Memorial Price in Economics.

Figure 2‑1: Relationship of Intrinsic value factors to market price.

From the 1934 textbook Security Analysis [8].

2.2 Modern Asset Pricing

2.2.1 Consumption-Based Model

In this thesis I reference the textbooks by two leading scholars, John Cochrane of University of Chicago [10] and John Y. Campbell [11] of Harvard University, extensively on the topic of asset pricing and I will avoid repeating the references unnecessarily. They both view asset pricing theory as a framework to understand the price of some claim to an uncertain (future) payment. The concepts described here are generalizations of the theory developed from Markowitz and onwards. I present it here in a top-down approach to arrive at the models used in this thesis and that form the basis of modern asset pricing.

The fundamental concept in all asset pricing, from stocks to bonds to options, is this: price equals the expected discounted payoff. The investor must choose how much to consume now and how much to save for tomorrow. The marginal utility loss of consuming less today and buying some asset should equal the marginal utility gain of consuming more of the asset’s payoff in the future. If the price and the future payoff does not satisfy this condition the investor will either buy more of or sell the asset. The investor’s first order condition for optimizing that choice leads to the consumption-based asset pricing model:

In the case of a stock the expected payoff x at a given time is the expected price plus the expected dividend payment at this given time. We treat the payoff as a random variable which can take many possible outcomes. The utility function u may take any form we’d want, e.g. , and describes the benefit, worth or value the investor gets from consumption at a given time (now or future). U is also treated as a random variable because we don’t know how much money we have tomorrow and thus how much we want to consume it. The beta is here used as a subjective discount factor to correct for the fact that investors are risk averse and impatient, preferring money now over a risky and delayed cash flow. We typically separate certain terms into a stochastic discount factor m which measures the investor’s “hunger”; the marginal utility of consumption in the future instead of today (or how much he values additional wealth tomorrow):

As a side note, most asset pricing models, like CAPM, ICAPM or APT, can be derived as special cases from the pricing equation (1) by imposing different constraints and form to the stochastic discount factor. For example, in the CAPM the discount factor is assumed to be a linear function of the return on a “wealth portfolio” R^w (often proxied by a stock market portfolio like S&P500).

Consider that we have a certain risk-free rate; then the discount factor becomes , which is the more “standard” discount factor often used. We can write the price of a specific asset i as below in equation (3) using the definition of covariance. And using the fact that expected discounted excess return should be equal to zero, derive the expected excess return R^e (4):

These derivations lead to the fundamental insight that the asset’s price and its expected excess return (risk premium) depend whether the payoff/return covary positively or negatively with the investor’s stochastic discount factor. As consumption c increase, the marginal utility m declines (diminishing return). If the asset payoffs x also declines together with m it implies a higher asset price. If payoffs covary negative with m investors will be willing to pay a lower price.

The insight can be explained from risk aversion; if the investor holds an asset that has a positive covariance with consumption, i.e. pays off well when you feel rich and pays less when you feel poor, it will make the consumption stream more volatile. A negative covariance between returns on the other hand will reduce consumption volatility and the investor can keep a steady consumption even in bad times. Essentially, we value assets that pay us when we are most “hungry” for money. The variance of the asset payoffs themselves are irrelevant and does not generate a risk premium; the investor cares only about volatility in his own consumption.

2.2.2 Expected Return-Beta Model

Traditional asset pricing models, like CAPM, ICAPM and APT, often measure the investor’s “hunger” by evaluating the behavior of large asset portfolios. This evaluation is done by manipulating the pricing equation above to allow representing expected return by betas which are suitable for linear regression (note removal of excess return and that time subscript is removed):

Worth noting here is that the l is not asset specific and often interpreted as the price of risk, whilst the b is asset specific and the quantity of risk in each asset. Gamma is the inverse of E(m). For practical purposes we often wish to use factors that are not direct measurements of consumption growth. This goal can be achieved by introducing the concept of “factor-mimicking portfolios”, in which we select a portfolio of assets whose payoff or return correlate closely with the discount factor m. The payoff space X is the set of all payoffs that investors can invest in and where investors can form any portfolio of traded assets or linear combinations of payoff vectors. Thus, a portfolio can be represented as vector of payoffs (e.g. return on S&P500 stocks) and the payoff space consist of , where c is a vector of portfolio weights. To mimic the stochastic discount factor, we must choose a vector which should be the orthogonal projection of the m onto X. We do this by choosing , such that (dropping vector notation) . This implies is our discount factor to price the basis assets in x.

This discount factor is called the mimicking portfolio for m and is holds the same pricing implications as m, i.e. we can substitute all the m’s in equation 5 with x*. Using the same arguments, we can create any factor f in which the factor-mimicking excess returns is the orthogonal projection of vector f onto the excess return space R^e. We can use the model form of equation 5 with the betas being regression coefficients of the returns on the factor-mimicking portfolio (not the factor itself). When using return as a factor the model becomes very elegant, since the factor risk premium is also the expected excess return.

By expand the model and saying b and l is a linear combination of a sum of b_k and l_k we end up with the expected return-beta model form we will use in this thesis:

In the cross-sectional regression above the b_k’s are the exposure of asset i to risk factor k and l_k is the expected return for each unit of this exposure. We can also run a time-series regression for each asset i where beta are the coefficients we get when running a regression of return on factors. The factors i are (or should be) proxies for marginal utility growth:

2.2.3 Selecting factors – market anomalies

When generating a factor-mimicking portfolio, the analyst will look for factors that have predictive power on future returns. As described above we can trivially fit an unlimited number of factors to suit the return space data. So, to quote Cochrane the challenge is that:

“Most empirical asset pricing research posits an ad hoc pond of factors, fishes around a bit in that pond, and reports statistical measures that show ‘‘success,’’ in that the model is not statistically rejected in pricing a set of portfolios”

So how do we combat this? According to Cochrane the best advice is to understand fundamental macroeconomic sources of risk, use economic theory to carefully specify the factors applied and use cross-sample and out-of-sample checking of your model’s stability. The purpose is not necessarily to have a perfect data fit, but to describe how the investor’s “hunger” varies along axes of interest in the cross-section and/or in time.

Factors that do not fit into the effective market hypothesis or CAPM framework have historically been called market anomalies, styles or risk factors. William Sharpe [12] was one of the many early researchers who suggested that the main differences in portfolio (mutual fund) returns could be attributed to differences in exposure to the four asset classes value/growth and large/small cap and he used factor models to show it. Most famous is of course the three Fama-French factors (market, size and value) and the later addition of momentum by Carhart [13], which have become the benchmark models used in empirical research.

Hou et al. [14] studied market anomalies extensively using cross-sectional data in a critical review, where they replicated 447 anomaly variables reported in financial literature. This research field is very prone to data mining (e.g. statistical overfitting or using of illiquid stocks), so after replicating the cross-sectional regression analyses for each factor the researchers found that only 161 were significant at a “typical” 5% significance level and only 46 when applying a more strict criteria as recommended for this type of analysis [15]. There is no commonly accepted classification of the market anomalies, but some of the most significant cross-sectional categories include:

Factor	Description
Momentum	The phenomenon that securities which have performed well relative to peers (winners) on average continue to outperform, and securities that have performed relatively poorly (losers) tend to continue to underperform [16].
Value	Value is the phenomenon that securities which appear “cheap” on average outperform securities which appear to be “expensive” [17].
Investment	A negative relation between capital investments for a firm and its future returns.
Profitability	An observation that more profitable firms have higher expected returns than less profitable profitable firms.

It is interesting to note that even with all the developments in data availability and computing power it seems like many of the experience-based guidelines Benjamin Graham gives in his book “The intelligent investor” [18] are still valid and actually resemble many of the significant predictive factors found. Graham advises the intelligent investor to select stocks that have a low risk of default, low debt-to-asset ratio, high asset-to-liability ratio, at least five years of earnings growth, low price-to-earnings ratio, low price-to-book ratio and who are paying dividends.

In order to avoid the pitfalls of selecting factor models that result from data mining or other misuse of statistics and data several authors have in recent years provided guidelines and heuristics. Both Hsu et al. [19] and Arnott et al. [20] provide guidelines for good which can be summarized as:

· Establish an ex-ante economic foundation

· Factors should be robust across definitions and geographies (cross-validation)

· Do not ignore trading costs and fees

· Ensure good data quality and document data transformations

As ever, it pays to listen to the advice of the old masters, here from Albert Einstein (1933):

“It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.”

2.3 Quality as a Factor

2.3.1 Overview

In this thesis I will focus on investigating the factor, or investing style, called quality. It refers to a hypothesis (and finding) that investing in highly profitable, operationally efficient, safe and stable companies tend to outperform the market over time. There is no good common definition of quality across the literature, but Asness et al. [1] made a good attempt by defining quality as “the characteristics that investors, all else held equal, should be willing to pay a higher price for”.

Then, what would those characteristics be? NBIM [21] review the quality factor and find that the factors considered in the literature can typically be grouped into three categories; profitability, safety and quality of earnings. Asness et al. also review existing literature and arrive on a very similar grouping. Because Asness et al. justify their quality model with a more theoretical first principles approach that fits into a modern asset pricing framework I will use their grouping in the following:

· Profitability
The economic reasoning is that, all else equal, highly profitable companies should command a higher stock price. Profitability refers to the ability to generate earnings compared to expenses and can be measured by many accounting ratios. Hou et. Al [14] found 41 significant profitability-factors, typically related to ROE, ROA, gross profit to assets, asset turnover, operating profits to assets and cash-based operating profits to assets. Generally, these accounting factors indicate how well the company is deploying its capital to generate return and how well it manages its expenses.

· Safety
The basis of safety characteristic is that, all else qual, investors should a higher price for companies with a lower required return (when looking at the companies’ discounted cash flow). Risk of default by for instance excessive leverage would by economic theory increase the financing cost of a firm and thus the required return. Typical factors that describe the safety of a company are often related to a strong balance sheet, like low debt-to-assets, high current ratios, or volatility of profitability factors.

· Growth
Growing profits are considered a characteristic that investors should pay a premium for, all else equal. This growth can typically indicate that the company has a sustaining competitive advantage over the competition. It can be measured as X-year growth in profitability (measured as above) or considering volatility over time.

Additionally, it is important to bring up research that failed to find a statistically significant “quality factor”. Beck et al [22] found that the individual constituents of a typical quality factor does not have any explanatory power on return and risk of stocks. This result either disproves quality as a factor or it could be that it is the interaction between the quality variables that makes it a predictor of future returns.

2.3.2 Model for Quality

Asness et al. derive a mathematical model for quality using the firm value (price) described as the present value of all future dividends as a starting point (as described in section 2.2):

The important point to note here is their choice of stochastic discount factor (also called pricing kernel), in which is the zero-mean innovation to the discount factor. When computing the conditional expectation of the discount factor they end up with . This implies that firm value is priced using a discount factor which is constant across time, which is an assumption we know to be an important simplification (see Cochrane [23] for a great review of the time-varying discount rate). We know that interest rates vary a lot over time and the expectation of future interest rates will greatly affect the discount rate and subsequently the prices. This choice of discount factor could lead to a model that does not account for changing interest rate regimes.

In the following I use value V instead of price p to keep the same terminology as in the paper. After some derivations and using the residual income valuation model Asness et al. compute the fundamental firm value as the sum of the book value and all future discounted residual incomes, which as a fraction of book value becomes the following:

Value profitability growth safety (negative risk)

Using this model founded on “first principles”, we see that the firm’s value can be explained by factors relating to its ability to generate profit, growth and avoid negative risk, which was hypothesized in the previous chapter. Other authors, e.g. Frama and French (2014) [24], starting from the same dividend growth model end up with slightly different factor models although the reasoning is similar.

The next step in developing the factor model is to find representative proxies for the variables in the equation above. We are not looking to price assets correct in absolute values, but to compare prices relative to each other. Asness et al. use the result from robust studies to select available fundamental data points for companies and to construct proxies for profitability, growth and safety. For instance, the profitability measures used have been mostly selected from a highly cited study by Novy-Marx [25]. Each variable is ranked in the cross-section universe, normalized (z-scored) and given equal weight when averaged into a factor, which is normalized on its own.

The following table provides a summary of the variables. The growth variables with a delta-prefix indicates the 5-year change of the variable. To see how I have constructed these measures in the analysis I refer to the Python notebook’s section 2.2 in Appendix 3.

Table 2‑1: Variable definitions

Variable	Description	Variable	Description
GPOA	Gross profit over assets	BAB	Market beta
ROE	Return on equity	LEV	Leverage (debt over assets)
ROA	Return on assets	O	Ohlson’s O-score
CFOA	Cash flow over assets	Z	Altman’s Z-score
GMAR	Gross margin	EVOL	Earnings volatility
ACC	Fraction of cash earnings

3 Data

3.1 Quantopian Research Platform

For all the data analysis in this thesis I have used Quantopian.com, which provide a cloud-based data science platform for performing quantitative financial analysis using the Python programming language. The platform provides an IDE (interactive development environment) to perform research on equity data and an engine to perform backtesting of trading algorithms.

3.2 Data Sources

The data available through Quantopian contain quality checked equity data from 44 countries from 2004-2019. For example, to avoid survivorship bias they contain data as stocks are listed and delisted and stored point-in-time so that the backtesting simulation engine avoids any lookahead bias. As an example, in asset pricing research it is fairly customary to construct factors based on accounting data with a six months’ time lag to avoid lookahead bias. With point-in-time data this is not necessary because data in the backtesting engine will only become available in the simulation at the historical filing date of each company’s financial reporting.

The data sources used in this thesis are from FactSet and contain fundamentals data, equity pricing and metadata and RBICS (business industry classification). To expand the analysis the available data also range from analyst estimates to insider trade transactions and news sentiment.

3.3 Data Processing

Although the data sources are of high quality, they still must be processed in order to obtain sample data that can be analyzed and that are relevant. The first data screening is to remove any non-tradable assets and to only include primary shares. The primary share is defined as the first share/ticker that a company has at IPO and is still actively trading. If this share is no longer trading, the share with the highest volume is denoted as the primary share. After this initial filtering, we typically see that the datasets contain up to 10-30% of missing data for some of the accounting/fundamental data that we use to build the quality factor. This is typically the smaller stocks that we anyway almost disregard when value-weighting the components later in the analysis work. Some data is critical, so any stock with missing market to book ratio has been completely removed.

The next step of processing is to build all the quality factors given in section 2.3.2. First, we perform a winsorization to limit the effect of extreme values and possible spurious outliers (especially relevant for accounting data and ratios). 95% winsorization is done by setting all values outside the lower and upper bound (2.5 and 97.5 percentile) equal to the boundary value.

Next, we know that accounting data is different when comparing across industries. For example, the profit margin is typically much higher for companies in the financial sector than in the utilities sector (although this tells us little about the returns from investing in either industry). To normalize accounting data across industries we demean each factor my sector. This means that the most profitable investment bank is ranked equal as the most profitable utility company when constructing the profitability factor. There are several choices on methodology for industry demeaning and each one has its positive and negative sides. Some researchers eliminate all financial services firms from the analysis, they cluster regressions by industry or they enforce sector neutrality by weighting methods. For this work I have chosen to demean by grouping all stocks within each sector together and then normalizing each of the factor components within sectors. The dataset groups each asset in one of 13 industries, but unfortunately industry classification is missing for a lot of the smaller markets (again, this is most widespread in small stocks). Comparing results before and after industry demeaning showed a marked improvement when inferring statistical significance of the regressions.

When normalizing (z-scoring) the fundamental data we assign the stocks with missing data to have a score of zero, such that when we aggregate the normalized factors the missing data for each stock is effectively ignored. The method may not be perfect, but for empirical research it serves the purpose of not having to delete every stock which is missing some data which would reduce our sample data. Finally, the stocks are ranked and then normalized as suggest by Asness et al. When the procedure in this section has been performed, we are left with zero missing data for the analysis work.

3.4 Summary Statistics

The 44 countries analyzed are listed below, sorted by size along with some summary statistics. All the countries have been analyzed from 2005 until June 2019 and consist of a total of 49 003 companies.

The market capitalization time series is converted to US dollars using London Market spot exchange rates at close of each day and the mean value here is across the entire time series. The number of stocks per month is the number included in each monthly calculation and the total stocks is the total number of unique assets over the entire time period. The global market weight is a naive calculation of each countries relative size as the weighted average of the mean market cap multiplied by number of stocks per month. For comparison I have also made a column for each countries weight based on the number of stocks in each universe divided by total number of stocks.

Table 3‑1: Summary statistics of data sample

Country	Mean Market Cap	Stocks per month	Total Stocks	Global Market Weighted Size	Global Equal Weight Size
United States	4.15E+09	4502	6866	34.9 %	14.0 %
Great Britain	1.78E+09	1723	3820	8.3 %	7.8 %
Japan	1.17E+09	3723	5092	7.3 %	10.4 %
Hong Kong	2.32E+09	1454	2493	7.1 %	5.1 %
China	1.30E+09	2143	3575	5.7 %	7.3 %
Canada	6.59E+08	2554	4887	3.9 %	10.0 %
Germany	1.80E+09	846	1503	3.3 %	3.1 %
Australia	6.99E+08	1680	2866	2.5 %	5.8 %
South Korea	6.54E+08	1571	2620	2.1 %	5.3 %
Switzerland	4.40E+09	242	374	2.0 %	0.8 %
Russia	2.78E+09	236	543	1.9 %	1.1 %
Spain	4.67E+09	158	319	1.8 %	0.7 %
Sweden	1.17E+09	485	1132	1.6 %	2.3 %
Taiwan	4.88E+08	1647	2379	1.4 %	4.9 %
Brazil	2.92E+09	174	283	1.0 %	0.6 %
Netherlands	4.10E+09	107	201	1.0 %	0.4 %
South Africa	1.28E+09	312	602	0.9 %	1.2 %
Singapore	6.94E+08	678	1018	0.9 %	2.1 %
Mexico	3.17E+09	116	196	0.8 %	0.4 %
Norway	1.07E+09	241	500	0.7 %	1.0 %
Indonesia	7.42E+08	428	660	0.6 %	1.3 %
Malaysia	3.77E+08	943	1294	0.6 %	2.6 %
Denmark	1.61E+09	169	280	0.6 %	0.6 %
Thailand	5.23E+08	564	834	0.5 %	1.7 %
Finland	1.67E+09	128	203	0.4 %	0.4 %
Turkey	6.68E+08	321	472	0.4 %	1.0 %
Poland	3.46E+08	442	760	0.3 %	1.6 %
Colombia	2.64E+09	47	82	0.3 %	0.2 %
Austria	1.69E+09	76	127	0.3 %	0.3 %
Philippines	6.98E+08	230	303	0.3 %	0.6 %
Argentina	1.41E+09	78	116	0.2 %	0.2 %
Ireland	2.48E+09	33	64	0.2 %	0.1 %
Greece	3.78E+08	243	363	0.2 %	0.7 %
Portugal	1.44E+09	52	89	0.2 %	0.2 %
Peru	6.16E+08	120	191	0.1 %	0.4 %
Czech Republic	1.97E+09	19	55	0.1 %	0.1 %
New Zealand	4.26E+08	126	223	0.1 %	0.5 %
Pakistan	2.14E+08	246	342	0.1 %	0.7 %
Hungary	7.23E+08	35	64	0.1 %	0.1 %

4 Analysis

4.1 Overview

In order to answer my three main research questions and to replicate the “Quality minus junk” study I will perform the following analyses to test each hypothesis:

1) There is a positive correlation between price and quality

a. Persistence of quality

b. Regression of price on quality

2) There is a positive risk-adjusted return from investing in (going long) high-quality stocks and shorting the low-quality stocks

a. Regression of excess return on quality sorted portfolios

b. Regressions of the QMJ factor-mimicking portfolio returns on risk factors.

4.2 Correlations Between Factor Components

The following plots show the relationship between the quality factor and its sub-factors profitability, growth and safety and the relationship between each sub-factor and their individual components. The pairwise correlations for the global sample mean weighted by market size is found in Table 4‑1. The main finding you can see graphically from Figure 4‑1 is the strong pairwise correlation coefficients between the quality components. The correlation between profitability and growth of 0.67 across the whole global value weighted sample indicate that profitability is persistent and this is in line with findings from Novy-Marx [25]. It is less intuitive that profitability and growth is correlated with the safety factor and from these initial plots and the average numbers across the sample it difficult to see any patterns (on average profitability and safety have a correlation coefficient of 0.11).

From Figure 4‑2 to Figure 4‑4 we see that there looks to be a positive relationship between all the components (fundamental data) that make up a factor, which tells us that Asness et al. found a robust set of proxies for their factors. By robust I mean that if some data constituting e.g. the safety factor is missing or has measurement error it will have less effect on the aggregated main factors. It should also be noted that the factor sub-components are not shown in their normalized form and that the underlying sample distributions of fundamental data are very much non-normal.

Table 4‑1: Pearson product-moment correlations between quality and sub-factors

	Quality	Profitability	Growth	Safety
Quality	1.00			0
Profitability	0.82	1.00
Growth	0.73	0.62	1.00
Safety	0.48	0.12	0.07	1.00

Figure 4‑1: Quality plotted against its sub-factors profitability, growth and safety.

The diagonal shows the sample distribution of each factor along with a fitted regression line to indicate direction of relationship. Pearson product-moment correlations are denoted by R-value. Data is US sample from ’05-‘19.

Figure 4‑2: Pair-plots of the profitability factor and its sub-components.

The diagonal plots are the sample distributions and the off-diagonal scatter plots also show a fitted regression-line to indicate direction of relationship. Pearson product-moment correlations are denoted by R-value. The sample is US stocks ’05-’19

Figure 4‑3: Pair-plots of the growth factor and its sub-components.

The diagonal plots are the sample distributions and the off-diagonal scatter plots also show a fitted regression-line to indicate direction of relationship. Pearson product-moment correlations are denoted by R-value. The sample is US stocks ’05-’19

Figure 4‑4: Pair-plots of the safety factor and its sub-components.

The diagonal plots are the sample distributions and the off-diagonal scatter plots also show a fitted regression-line to indicate direction of relationship. The sample is US stocks ’05-’19

4.3 Regression Analysis

In the following sections we run regression analyses on price and on returns. Our main tool is ordinary least-squares regression, but we use the procedures of Fama-Macbeth to obtain corrected standard errors and correct for autocorrelation using the method of Newey-West. Although these are the traditional tools used in asset pricing research (and by Asness et al.) the more modern approach, summarized nicely by Peterson [26], would be a panel regression with clustered standard error estimates for firm effects and time. Thompson [27] builds on this approach and provides simple formulas for firm and time effect corrected standard errors. The bias of the Fama-Macbeth standard error is most severe in cases where a persistent dependent variable is regressed on persistent independent variables, for example when we regress the market-to-book ratio on firm characteristics.

Despite this, because I struggled to implement clustered errors in the Python Statsmodels regression library (and to stay true to Asness et al.’s methodology) I chose to use the Fama-Macbeth procedure described here.

The procedure is slightly different depending on what our factors are. For observable characteristics the first step below is often omitted or taken as a separate analysis. In our case we do regressions on quality, which is calculated separately for each asset and each time step. So, there is no need to estimate asset-specific betas using equation 14 below.

The Fama-Macbeth two-step regression procedure is often used in analysis of factors that explain asset returns. It is a practical “two-pass” way of testing how the factors describe portfolio or asset returns by finding the return premium from exposure to the factors. First, each portfolio’s or asset’s return is regressed against the factor time series (e.g. MKT or QMJ) to determine how exposed it is to each one using equation 14.

In a “traditional” two-step regression, we would then use equation (15) to estimate a single cross-sectional regression with the sample averages, but Fama-MacBeth suggested that instead we run a cross-sectional regression at each time period. The main advantage of Fama-MacBeth is to then average these coefficients, once for each factor, to give the premium expected for a unit exposure to each factor (19) and alpha (17) over time. This method splits the sample into T smaller samples and we can deduce the variation across samples (time), assuming no autocorrelation. Our estimators simply become the average across time (sample mean) and the sampling errors are generated from the standard deviation of the sample means:

If the prices are independent and identically distributed (iid) normally over time, then the t-statistic can be used to test the null hypothesis that the regression coefficients are zero. See Cochrane [10] chapter 12.3 for a detailed treatment of the procedure. The practical implementation of this second step is to run a regression of the periodic estimates against a constant and use the software option for Newey-West heteroskedasticity and autocorrelation adjusted standard errors. The estimated coefficient of such a regression is simply the sample mean (as above) and corrected standard errors. The Newey-West procedure requires the user to set a number of time lags to use in the correction and according to literature [28, p. 7] a guideline for choice is to follow this equation when using the Bartlett kernel (which is what Statsmodels uses as default):

4.4 Portfolio Forming

Before digging into the analysis of quality-sorted portfolios, I will briefly explain the method used. Portfolio analysis is traditionally a very commonly used method in empirical asset pricing to examine the cross-sectional relationship between some variable(s). It is essentially a non-parametric cross-sectional regression using non-overlapping histogram weights, as illustrated in Figure 4‑5. The big motivation for creating portfolios is to remove the “noise” (idiosyncratic volatility) of each individual asset by bundling them into portfolios of assets that have relatively similar exposure to a factor. The univariate portfolio analysis procedure has, as detailed nicely by Bali et al. [28], four steps:

1) Calculate the factor breakpoints that will be used to divide the sample into portfolios.

2) Use these breakpoints to form the portfolios.

3) Calculate the average value of the outcome variable Y within each portfolio for each period t and present the time series average with corrected standard errors.

4) Examine the variation in these average values of Y across the different portfolios.

a. Examine if the time-series mean of the portfolios, especially the difference portfolio (H-L), is statistically different from a null hypothesis mean value (often zero). A non-zero mean is evidence that a cross-sectional relation exists between the sort variable and outcome variable.

There are also methods for creating bivariate (double-sorted) portfolios, which is what Asness et al. does when creating the QMJ factor by sorting on size (market capitalization) and then sorting on the quality factor. This bivariate sort is similar to a regression on quality controlled for size. According to Cochrane [10] you can get the same results whether you perform portfolio sorts or multivariate regression in time and cross-section (panel data regression). This is what Figure 4‑5 shows by comparing a regression slope and the portfolio mean values in a factor model on returns with log(book/market cap) as the only factor variable. The challenge with portfolio sorting is when your factor models starts to have more than 2-3 factors which should all be sorted on. Ang, Liu and Schwarz [29] actually find that the practice of portfolio forming leads to larger standard errors of cross-sectional coefficient estimates because it reduces the information (beta dispersion). Nevertheless, because Asness et al. use double sorted portfolios in their paper I have done the same.

Figure 4‑5: Portfolio mean return versus cross-sectional regressions [23].

4.5 The Price of Quality Stocks

4.5.1 Persistence of Quality

In order to determine the price of quality stocks I first perform a univariate portfolio sort on quality to split each stock universe into ten equal-sized quality portfolios. This is the first step of testing whether high quality firms command higher prices. If quality is persistent it means the market can predict future quality and take this into account when determining the prices today.

The results from Table A-1 in Appendix 1 show us that the quality score is consistent over time for the entire sample. This is also illustrated visually in the figures below. Figure 4‑6 shows the difference portfolio (high minus low) for each country in the sample at the time of portfolio formation and three and ten years after formation. Each month we form the quality sorted portfolios and record the quality scores of the same portfolio three and ten years later. We examine if the time series mean of the difference portfolio after three and ten years is statistically distinguishable from zero as an indication/evidence that a cross-sectional relationship is persistent. This is done by regressing the time series means on a constant and implementing the Newey-West adjusted standard errors to correct for heteroskedasticity and autocorrelation.

We also want to know if there is a monotonic pattern in the quality sorted portfolios. Figure 4‑7 shows the average portfolio quality means for the entire sample. At portfolio formation the monotonicity is by construction, but we also see that the monotonic pattern is persistent even after ten years. There is a regression towards the mean, but we clearly see that on average a significant number of the high-quality companies at portfolio formation are still winners even ten years later and vice versa.

The combined results allow us to conclude that quality is persistent is every country of the sample and that it is possible to select companies which will exhibit high quality in the future by looking at their recent past. In theory that should mean that the market has the necessary information to correctly reflect future quality in today’s prices.

Figure 4‑6: This chart shows the high-minus low of quality sorted portfolios

at time of portfolio formation and the corresponding mean portfolio quality scores 3 and 10 years after portfolio formation. All estimates are statistically significant; the average t-statistics for the 3-year lagged means is 32.61 and for the 10-year lagged means it is 15.72.

Figure 4‑7: Change in mean portfolio quality scores from time of formation

and after 3 years and 10 years. Portfolio scores are the equal weight mean of the entire global sample.

4.5.2 Price of Quality in the Cross-Section

We now run a cross-sectional regression of price on quality. Although it varies from the expected return-beta model its equivalence can be seen by examining equation 3 to 5.

We perform the natural logarithmic transformation of highly skewed ME/BE data into “close to” normally distributed data, but to avoid numerical issues I applied to the market equity to book equity (the regressand). The interpretation is, according to Woolridge’s textbook on econometrics [30, p. 193], approximately same as in a standard log-linear regression model where a unit change in X leads to 100×β% change in Y. Because our factors are z-scored a unit change in our factors is equal to a standard deviation change, e.g. moving up from the mean quality score to the 84th percentile. I have run regression models without the log-transformed dependent variable and the results are similar (coefficients still strongly significant). The cross-sectional regressions are performed using the Fama-Macbeth procedure as described in section 4.3. We run five different model specifications: four regressions of price on quality, profitability, growth and safety individually and a fifth multivariate regression of price on profitability, growth and safety. To get a visual understanding of the sample I have included Figure 4‑8 which shows the underlying sample data scatterplot of price and quality along with a fitted regression line and the sample distributions for the US market.

Figure 4‑8: Typical scatterplot of time averaged sample data and fitted regression line

(US ’05-’19). Distribution of Samples shown on top and right along with Pearson’s correlation number (0.27) between the two variables

From Table 4‑2 we see that our hypothesis stating that there is a positive correlation between price and quality cannot be rejected for the big majority of countries. Our regressions show significant coefficient, all our sub-components of quality have the same sign and the results are in general in alignment with Asness et al. Although I have not included all the controlling factors that they have I find the explanatory power of the regressions to be in the same range as their study, with about 8% of variation explained in the US sample and 8% in the value weighted global sample. The magnitudes of the coefficients are in the same order of magnitude and the aggregation of sub-components into the quality score retains both magnitude and statistical significance. Given that our starting point was a theoretically plausible formulation of a firm’s fundamental value it is perhaps surprising that a regression model made of the components profitability, growth and safety explain very little of the cross-sectional variation in prices. But nonetheless, we can conclude that higher quality companies do command higher prices than “junk” companies.

Looking at the magnitudes, Figure 4‑9 zooms in on the quality slop estimate for the sample. First, we see that the magnitude varies, but the majority of countries exhibit a statistically significant positive relation with a value weighted sample mean of 0.11. This is interpreted such that if the quality score of a company moves one standard deviation higher, ceteris paribus, the market to book value (ME/BE) ratio only increases 11% from the total sample. Or put differently; companies having a quality score in the 99^th percentile (2σ) can enjoy only a 22% higher stock price than the average company (all else equal, particularly book equity). The slope coefficient estimated for quality is much lower than the 0.22 and 0.24 coefficient that Asness et al. finds, but their sample is much longer and could indicate that relationship between price and quality is lower in more recent years. For the Norwegian reader it is worth noting that the slope coefficient for the Oslo Stock Exchange is on the lower side at 0.05 (with a t-statistic of 12.57), i.e. the price of quality in Norway is low compared to the global sample.

Our analysis on the relationship between price and quality leaves us to conclude that our model specification for quality does explain prices, i.e. our first hypothesis that high-quality firms exhibit higher prices cannot be rejected for 40 of our 44 countries. The findings here confirm and support the results from Asness et al.’s study on the quality factor.

Figure 4‑9: This chart’s left-hand axis shows the slope coefficient estimates for a regression of price on quality for each country.

The crosses indicate the t-statistic for each regression and the t-values are given on the right-hand axis scaled by log₂, which means that all the estimates with crosses below the main horizontal axis have a t-statistic less than 2.0 (ireland and phillipines).

Table 4‑2: The price of quality - Cross sectional regressions

This table presents the results from monthly Fama-Macbeth regressions. The dependent variable is the natural logarithms of a firm’s market-to-book ratio plus one at time t. The explanatory variables are the quality scores at time t. AdjR² is the time series average of the adjusted R-squared of the cross-sectional regressions of price on quality (model 1). Standard errors are adjusted for heteroskedasticity and autocorrelation using a lag length of 5 periods. T-statistics are shown below the coefficient estimates in paranthesis. The top row shows the global sample mean by market size weights. Countries as sorted by market size from big to small.

	(1)	(2)	(3)	(4)	(5)			Adj R^2
	Quality	Profitability	Growth	Safety	Profitability	Growth	Safety
Sample mean	0.11	0.08	0.06	0.11	0.06	0.02	0.10	0.06	171	2363
United States	0.19	0.15	0.15	0.12	0.10	0.07	0.10	0.079	119	4133
	(54.74)	(28.84)	(22.13)	(23.84)	(20.64)	(7.28)	(14.71)
Great Britain	0.13	0.06	0.00	0.20	0.10	-0.04	0.20	0.028	172	1652
	(26.29)	(7.25)	(-0.73)	(46.75)	(6.73)	(-3.14)	(40.65)
Japan	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.062	163	3723
	(11.00)	(13.37)	(0.00)	(0.00)	(17.56)	(-8.50)	(0.00)
Hong Kong	0.04	0.01	0.02	0.07	-0.01	0.01	0.07	0.022	168	1440
	(29.47)	(3.58)	(19.38)	(24.14)	(-2.12)	(2.22)	(23.50)
China	0.06	0.03	0.04	0.07	-0.03	0.05	0.08	0.034	165	2126
	(15.05)	(7.82)	(11.44)	(10.25)	(-5.58)	(10.32)	(10.23)
Canada	-0.01	-0.11	-0.08	0.18	-0.06	0.01	0.18	0.000	172	2334
	(-0.37)	(-7.23)	(-5.81)	(11.70)	(-3.51)	(0.75)	(16.06)
Germany	0.11	0.06	0.02	0.16	0.04	0.00	0.16	0.028	173	817
	(21.38)	(10.72)	(3.83)	(25.81)	(5.28)	(-0.23)	(24.69)
Australia	-0.01	-0.10	-0.07	0.15	-0.07	0.02	0.13	0.001	172	1620
	(-2.13)	(-12.78)	(-10.96)	(18.67)	(-8.86)	(2.52)	(20.44)
South Korea	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.015	167	1571
	(15.59)	(0.40)	(9.53)	(13.79)	(-5.74)	(8.26)	(11.70)
Switzerland	0.14	0.13	0.07	0.11	0.15	-0.05	0.10	0.077	171	239
	(24.00)	(17.69)	(10.55)	(20.13)	(13.43)	(-3.87)	(17.12)
Russia	0.04	-0.01	0.05	0.06	-0.08	0.08	0.06	0.010	168	234
	(7.30)	(-2.09)	(8.28)	(8.79)	(-8.51)	(9.68)	(6.34)
Spain	0.18	0.17	0.09	0.14	0.17	-0.04	0.10	0.069	174	154
	(13.05)	(11.40)	(6.61)	(16.22)	(9.57)	(-2.61)	(13.06)
Sweden	0.02	-0.03	-0.03	0.09	-0.01	-0.01	0.08	0.003	171	482
	(7.02)	(-7.74)	(-7.60)	(19.24)	(-1.70)	(-1.70)	(19.35)
Malaysia	0.08	0.07	0.04	0.07	0.07	-0.02	0.05	0.115	164	943
	(37.94)	(36.00)	(23.09)	(38.65)	(29.25)	(-15.81)	(28.57)
Taiwan	0.02	0.01	0.00	0.02	0.01	0.00	0.01	0.117	163	1647
	(34.43)	(23.15)	(14.21)	(26.99)	(18.84)	(-8.31)	(16.05)
Brazil	0.17	0.16	0.06	0.15	0.19	-0.07	0.12	0.109	168	170
	(20.66)	(12.88)	(7.53)	(15.30)	(11.55)	(-5.64)	(10.41)
Netherlands	0.08	0.03	-0.02	0.16	0.08	-0.07	0.16	0.016	174	105
	(5.43)	(0.00)	(-1.04)	(8.28)	(4.36)	(-2.31)	(7.77)
South Africa	0.04	0.04	0.02	0.03	0.06	-0.03	0.02	0.029	170	312
	(12.99)	(14.41)	(3.43)	(8.12)	(15.99)	(-4.61)	(6.18)
Singapore	0.12	0.09	0.06	0.11	0.08	-0.01	0.10	0.066	171	669
	(28.46)	(18.07)	(14.29)	(22.76)	(11.11)	(-0.93)	(16.53)
Mexico	0.03	0.04	0.02	0.02	0.04	-0.01	0.01	0.085	171	116
	(14.20)	(14.68)	(0.00)	(8.31)	(13.61)	(-4.12)	(0.00)
Norway	0.05	0.01	0.02	0.07	0.02	0.01	0.07	0.027	171	240
	(12.57)	(3.63)	(4.13)	(14.28)	(2.78)	(1.76)	(15.21)
Indonesia	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.062	165	428
	(21.75)	(20.17)	(18.42)	(11.93)	(6.36)	(5.29)	(9.60)
Denmark	0.10	0.08	0.05	0.09	0.08	-0.02	0.09	0.112	170	168
	(11.19)	(9.61)	(7.31)	(13.14)	(9.47)	(-2.89)	(15.12)
Thailand	0.01	0.01	0.00	0.01	0.01	-0.01	0.01	0.033	166	564
	(11.34)	(13.69)	(5.26)	(7.96)	(14.37)	(-8.31)	(6.56)
Finland	0.20	0.17	0.09	0.20	0.16	-0.04	0.17	0.142	171	126
	(34.89)	(23.79)	(10.51)	(43.00)	(13.33)	(-3.98)	(34.40)
Turkey	0.07	0.05	0.01	0.09	0.03	-0.01	0.08	0.020	171	317
	(9.94)	(8.75)	(1.14)	(14.78)	(7.45)	(-1.23)	(12.20)
Poland	0.09	0.06	0.01	0.12	0.05	-0.01	0.11	0.000	170	437
	(15.64)	(8.21)	(2.58)	(29.70)	(5.74)	(-1.83)	(27.61)
Colombia	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.058	166	47
	(8.77)	(10.28)	(5.30)	(7.42)	(9.65)	(-5.60)	(1.37)
Austria	0.14	0.12	0.05	0.15	0.14	-0.06	0.13	0.076	169	75
	(8.29)	(5.42)	(4.34)	(8.34)	(4.53)	(-3.05)	(9.59)
Philippines	0.00	-0.03	-0.01	0.05	-0.04	0.01	0.05	0.000	166	228
	(1.11)	(-7.22)	(-4.07)	(9.05)	(-7.86)	(3.61)	(9.52)
Argentina	0.06	0.07	0.04	0.04	0.07	-0.02	0.02	0.037	164	78
	(10.22)	(11.22)	(5.48)	(5.97)	(7.51)	(-2.02)	(3.15)
Ireland	0.03	0.05	0.02	0.00	0.11	-0.06	-0.02	0.000	173	32
	(1.86)	(2.43)	(1.27)	(-0.00)	(4.05)	(-2.80)	(-0.56)
Greece	0.19	0.16	0.08	0.19	0.12	-0.01	0.14	0.108	167	238
	(20.64)	(17.34)	(8.56)	(31.41)	(10.97)	(-1.11)	(30.07)
Portugal	0.15	0.15	0.09	0.09	0.15	-0.02	0.06	0.047	173	50
	(11.06)	(9.99)	(5.72)	(5.24)	(7.12)	(-0.85)	(3.75)
Peru	0.11	0.10	0.06	0.10	0.07	0.00	0.07	0.103	171	120
	(19.47)	(15.70)	(10.20)	(19.00)	(7.54)	(-0.40)	(10.66)
Czech Republic	0.01	0.02	0.01	0.00	0.02	0.00	0.00	0.000	171	19
	(5.70)	(6.73)	(6.08)	(-0.30)	(4.13)	(-0.38)	(-0.92)
New Zealand	0.12	0.02	0.06	0.16	0.02	0.04	0.16	0.043	171	122
	(13.74)	(2.08)	(6.01)	(11.25)	(1.55)	(4.78)	(10.34)
Chile	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.001	170	190
	(6.33)	(-1.97)	(-2.43)	(11.43)	(-1.62)	(-1.39)	(9.64)
Pakistan	0.01	0.01	0.01	0.01	0.01	0.00	0.01	0.070	167	246
	(20.33)	(14.38)	(13.22)	(23.94)	(7.74)	(0.31)	(23.69)

4.6 The Return of Quality Stocks

4.6.1 The Return of Univariate Portfolio Sorts on Quality

In the analysis on prices above we found that the price of stocks varies monotonically with quality. We now perform a similar portfolio analysis on excess return. Although higher quality firms command higher prices, higher quality should not provide any excess return. We use the method of section 4.4 to create the 10 quality-sorted portfolios. The results of the different regressions are reported in Table A-2 of Appendix 1. Because of computer memory restrictions I had to perform regressions on one country sample at a time and it is thus not possible to infer statistical significance of a global sample.

First, I calculated the value-weighted excess return of the portfolios averaged over time and the Fama-Macbeth method for estimates and standard errors. Asness et al. do not have any lag between the measured returns and time of portfolio formation, i.e. they make no assumption on the hypothetical investor’s holding period. Because we have verified the persistence of quality, I have not included a sensitivity study on the time lag between measured return and portfolio formation.

Secondly, I have performed regressions of the portfolio excess returns using three models: the CAPM market factor, the Fama-French 3-factor model and the Fama-French-Carhart 4-factor model. For each regression I have reported the regression constant alpha which is the average excess return that is not due to sensitivity to the risk factors in the model. The t-statistic of the alpha tells us whether the portfolio generates statistically significant average abnormal returns. We also report the adjusted R² for the 4-factor model regression, the Sharpe ratio of the portfolio’s excess returns and the information ratio for the 4-factor alpha – defined as the annualized alpha divided by its annualized standard deviation and which can be interpreted as the Sharpe ratio adjusted for hedging the four factor exposures.

The excess return for each portfolio is calculated using the Fama-Macbeth procedure by regressing the time series means on a constant and implementing the Newey-West adjusted standard errors to correct for autocorrelation. To obtain the alpha estimates on the CAPM, 3-factor and 4-factor specifications I run regressions of excess return on the factor combinations and report the intercept after controlling for the CAPM, Frama-French [5] and Fama-French-Carhart [13] risk factors in separate regression models. The risk factors are constructed for each country in line with the methodology of Asness et al. and the original authors.

Where the factor-mimicking portfolios are made up as follows:

Because the full panel data results in Table A-2 is quite big I have summarized the main findings into charts and included a short excerpt as Table 4‑3. From Figure 4‑10 we see the global average of mean portfolio excess returns for all countries which exhibit statistically significant difference portfolios(changing to an equal weight of country results does not change the interpretation). The very clear finding from the portfolio analysis confirms our research hypothesis that investing in high quality companies and/or shorting low quality earns a significantly positive excess return.

The difference portfolio earns an excess of 0.98% per month (12.4% annualized) and the results are monotonically increasing. Of our 44 countries we see statistically significant result in 21 countries, accounting for 64% of the global market capitalization. When controlling for market risk and the other common risk factors we see that the monotonicity across portfolios remain, but the abnormal excess returns of the difference portfolio is reduced from 98 to 70 basis points per month.

Figure 4‑11 shows the 4-factor alpha for our entire sample, split into those with statistically significant estimates and not. The number of countries with significant alpha estimates for the difference portfolio has decreased to 16 countries so we can only draw inference for those shown in blue in the chart. Of the countries with significant alphas the abnormal return varies from 68 to 242 basis points per month, which is a very large magnitude.

The Sharpe ratio is a performance measure of risk-adjusted return and is calculated as the excess return divided by its standard deviation. Table A-2, exemplified in Table 4‑3, show that this ratio increases with quality, The information ratio (IR) is usually a measure of portfolio returns in excess of some benchmark divided by its standard deviation, but Asness et al. calculate the IR as the 4-factor alpha divided by the standard deviation of residuals. Figure 4‑12 shows the global market size weighted mean values for Sharpe ratio and information ratio across the quality sorted portfolios. The chart tells us that not only do quality stocks provide a higher return, but they are also safer in the meaning that we get higher returns per unit risk when investing in quality stocks over “junky” stocks.

The results are in line with what Asness et al. finds in their table 3 and it supports our research hypothesis 2 – that there is a positive risk-adjusted return from investing in high-quality stocks and shorting the low-quality stocks. Asness et al. use these findings to support their argument that limited market efficiency explains why quality only explain asset prices to a limited extent. They argue that if high quality stocks earn a higher risk-adjusted return than low quality stocks it must imply that market prices fail to reflect the quality characteristics. Alternatively, quality is linked to risk in a way which is not fully captured by the safety sub-factor of quality. We will explore this in the next section.

Figure 4‑10: The chart shows market-weighted means of the countries with statistically significant difference portfolios for excess returns and 4-factor alphas.

The blue bars represent the global average excess return of the quality-sorted portfolios along with the difference portfolios high-low. The peach bars represent the global average abnormal alpha returns when regressing portfolio excess returns on the 4 Fama-French-Carhart factors.

Figure 4‑11: This chart shows the fama-french-carhart abnormal returns (alpha) for the regressions of the quality-sorted difference portfolio’s monthly excess return

on the Fama-French-Carhart four factors. The countries is blue have statistically significant alpha estimates, whilst the countries in peach are included only for reference as their estimates are not significantly different from zero.

Table 4‑3: Return on Quality - excerpt from Table A-2 showing two countries of interest

The table shows quality sorted portfolio excess monthly returns along with the difference portfolio high-low. The alphas are the intercept from time series regressions of the monthly excess returns using the CAPM, Fama-French 3-factor model and the Fama-French 4-factor regression models. Returns and alphas in monthly percentage, t-statistics are shown below estimates in paranthesis and 5% statistical significance is shown in bold. Sharpe ratios (run on excess returns) and information ratios (run on 4-factor alphas) are annualized.

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	H-L
Panel A: US Sample
Excess Return	-1.86	-1.13	-0.88	-0.90	0.33	-0.60	-0.22	-0.39	-0.20	-0.11	1.75
	(-1.73)	(-1.14)	(-0.97)	(-0.99)	(0.26)	(-0.74)	(-0.26)	(-0.50)	(-0.26)	(-0.14)	(3.68)
CAPM α	-1.18	-0.76	-0.29	-0.32	0.03	-0.07	0.19	0.06	-0.10	0.38	1.55
	(-2.36)	(-1.31)	(-0.69)	(-0.74)	(0.04)	(-0.20)	(0.54)	(0.16)	(-0.36)	(1.45)	(3.34)
3-factor α	-1.06	-0.25	-0.48	-0.26	-0.48	-0.07	-0.01	0.02	-0.19	0.08	1.14
	(-2.55)	(-0.49)	(-1.13)	(-0.67)	(-0.97)	(-0.24)	(-0.03)	(0.04)	(-0.58)	(0.27)	(3.60)
4-factor α	-0.95	-0.68	-0.52	0.00	-0.41	-0.07	-0.15	-0.12	-0.31	-0.18	0.77
	(-2.57)	(-1.08)	(-1.37)	(-0.02)	(-0.94)	(-0.22)	(-0.42)	(-0.39)	(-0.91)	(-0.67)	(3.23)
Sharpe Ratio	-0.63	-0.43	-0.36	-0.37	0.11	-0.27	-0.10	-0.19	-0.10	-0.05	1.96
Information Ratio	-1.14	-0.75	-0.77	-0.01	-0.55	-0.10	-0.21	-0.16	-0.42	-0.30	1.04
Panel B: Norwegian Sample
Excess Return	-0.35	-0.51	0.34	0.25	0.22	0.33	0.70	0.64	0.67	0.92	1.27
	(-0.54)	(-0.83)	(0.58)	(0.46)	(0.41)	(0.72)	(1.34)	(1.46)	(1.48)	(1.89)	(3.38)
CAPM α	-1.45	-3.84	0.87	0.64	0.57	0.47	0.84	1.17	0.52	1.31	2.76
	(-1.24)	(-1.35)	(1.71)	(1.22)	(1.42)	(1.49)	(2.21)	(2.60)	(0.72)	(3.54)	(2.28)
3-factor α	-0.36	-0.39	0.90	0.36	1.04	0.77	1.02	0.85	0.96	1.32	1.68
	(-0.59)	(-0.84)	(1.96)	(0.77)	(2.77)	(2.28)	(2.86)	(1.94)	(2.22)	(3.20)	(2.38)
4-factor α	-0.64	-0.41	0.86	0.19	0.97	0.39	1.00	0.85	0.82	1.25	1.89
	(-1.11)	(-0.81)	(1.71)	(0.42)	(2.64)	(1.04)	(2.45)	(2.00)	(1.82)	(3.42)	(2.87)
Sharpe Ratio	-0.18	-0.28	0.22	0.16	0.16	0.26	0.48	0.49	0.50	0.72	0.93
Information Ratio	-0.26	-0.21	0.50	0.12	0.75	0.31	0.64	0.54	0.51	0.95	0.73

Figure 4‑12: This chart shows the global market weight mean of the Sharpe ratios and the information ratios of quality-sorted portfolios

along with the difference portfolio (High-Low). The Sharpe Ratio is calculated on the monthly mean excess return of the portfolio and the information ratio is calculated on the intercept (alpha) of regressions of portfolio returns on the Fama-French-Carhart four factors.

4.6.2 The Return on the QMJ Factor

We now create the QMJ (quality minus junk) factor in the same way as Asness et al. The QMJ factor is created by taking the value weighted returns of the intersection of six portfolios formed on size and quality. Each month we form two portfolios, small and large, based on the available asset’s market capitalization. In their study they use a different breakpoint for US and global stocks, but I have used the 80^th percentile of market equity as breakpoint for all countries. Quality is sorted into ten portfolios and we define the top 30% as quality stocks and the bottom 30% as junk. QMJ then becomes:

With the factor returns we run a regression of QMJ on the Fama-French-Carhart risk factors and report the alpha from regressions on the CAPM model and Fama-French 3-factor model. Regressions are run for each time period and standard errors corrected as per the Fama-Macbeth procedure and corrected for autocorrelation using the Newey-West method.

The results are shown in Table 4‑4 for the full sample of countries. The key takeaway is that the QMJ factor delivers significant excess return and alpha with respect to the various risk factors. The alpha is the average excess return that is not due to sensitivity to the risk factors in the model. The t-statistic of the alpha tells us whether the QMJ portfolio generates statistically significant average abnormal returns. The excess monthly return is on average 0.24% (2.9% per year) among the countries with significant estimates and the abnormal returns (alpha) averaging at 0.31% and significantly non-zero for 32 of the 44 countries.

From the risk-factor loadings on MKT, SMB, HML and MOM we see that quality has significant negative exposures to all except the momentum factor (MOM). The negative exposure to market (MKT) and size (SMB) tells us that QMJ is long on low-beta and large stocks and/or short high-beta small cap stocks. QMJ is negatively loaded on the value factor (HML) which can be explained because quality is positively related to price whilst HML is long on cheap stocks. The exposure to momentum is small and not significant, but I kept it in the model for comparison with Asness et al. The Sharpe ratio is calculated on the excess returns, but the more interesting comparison is the information ratio which can be interpreted as the Sharpe ratio adjusted for hedging the other factor exposures. Figure 4‑13 shows us that across our entire sample the QMJ factor delivers a positive alpha (except Ireland) and information ratio, even considering our short time series of data.

Generally, the results on the QMJ factor match very well with what Asness et al.’s study on 24 countries found. A QMJ portfolio that is long high-quality and short junk stocks earn a large and significant abnormal return (alpha) when controlling for some of the most used risk-factors used in literature. From the factor loadings the QMJ portfolio appear safer and this is also supported by the high information ratio (Sharpe ratio after hedging for other factor exposures) above 1.

Figure 4‑13: QMJ 4-factor alpha information ratios.

This chart plots the Fama-French-Carhart adjusted information ratio of the Quality minus Junk (QMJ) factor.

Table 4‑4: Regressions of QMJ returns on risk factors.

This table shows the QMJ portfolio returns and factor loadings on the Fama-French-Carhart risk factors along with the intercept (alphas) of time-series regressions of monthly returns on the CAPM and Fama-French 3-factor model. Returns and alphas are monthly percentages and t-statistics are shown in parentheses under the coefficient estimates.Annualized Sharpe ratio is calculated on the QMJ portfolio excess return and the information ratio on the 4-factor alpha.

QMJ	Excess Return	CAPM α	3-factor α	4-factor α	MKT	SMB	HML	MOM	Sharpe Ratio	IR	Adj. R^2
Sample Mean	0.24	0.30	0.33	0.31	-0.06	-0.10	-0.16	0.09	0.67	1.06	0.38
United States	0.25	0.38	0.33	0.32	-0.10	-0.19	-0.27	0.04	0.58	1.39	0.71
	(1.97)	(3.95)	(4.75)	(4.23)	(-5.77)	(-6.01)	(-4.74)	(0.70)
Great Britain	0.64	0.66	0.71	0.62	-0.03	-0.01	-0.17	0.19	2.13	2.52	0.31
	(7.27)	(8.95)	(8.46)	(6.51)	(-0.99)	(-0.12)	(-5.07)	(3.04)
Japan	0.07	0.05	0.18	0.18	0.01	0.05	-0.32	-0.10	0.21	0.97	0.59
	(0.84)	(0.68)	(3.34)	(3.28)	(0.78)	(2.05)	(-12.52)	(-2.68)
Hong Kong	0.04	0.08	0.15	0.16	-0.08	-0.06	-0.16	-0.01	0.09	0.46	0.23
	(0.29)	(0.76)	(1.49)	(1.52)	(-3.35)	(-3.39)	(-3.38)	(-0.14)
China	0.13	0.22	0.36	0.40	-0.03	-0.08	-0.29	0.20	0.24	1.14	0.56
	(1.00)	(1.99)	(3.21)	(3.82)	(-2.46)	(-2.29)	(-6.90)	(2.23)
Canada	0.16	0.25	0.70	0.77	-0.17	-0.19	0.05	0.06	0.30	1.98	0.40
	(0.86)	(1.72)	(4.50)	(4.21)	(-5.09)	(-4.79)	(0.65)	(0.82)
Germany	0.42	0.44	0.54	0.52	-0.12	-0.23	-0.07	0.05	1.28	1.77	0.25
	(4.52)	(4.72)	(6.09)	(5.57)	(-4.10)	(-5.56)	(-1.73)	(1.04)
Australia	0.38	0.42	0.55	0.56	-0.12	-0.17	0.12	0.03	1.05	1.99	0.37
	(3.61)	(4.49)	(0.00)	(6.85)	(-5.94)	(-5.70)	(4.11)	(0.78)
South Korea	0.15	0.21	0.33	0.32	-0.06	-0.01	-0.17	0.07	0.34	0.81	0.17
	(1.16)	(1.68)	(2.55)	(2.54)	(-2.65)	(-0.37)	(-3.67)	(1.00)
Switzerland	0.35	0.33	0.31	0.32	0.03	-0.04	-0.14	-0.02	1.02	0.98	0.08
	(4.91)	(4.56)	(4.53)	(4.75)	(0.92)	(-0.88)	(-3.14)	(-0.36)
Switzerland	0.35	0.33	0.31	0.32	0.03	-0.04	-0.14	-0.02	1.02	0.98	0.08
	(4.91)	(4.56)	(4.53)	(4.75)	(0.92)	(-0.88)	(-3.14)	(-0.36)
Russia	0.22	0.29	0.36	0.38	-0.08	-0.01	0.13	0.31	0.24	0.45	0.14
	(0.70)	(0.94)	(1.44)	(1.68)	(-1.79)	(-0.10)	(2.35)	(2.17)
Spain	0.46	0.56	0.55	0.57	-0.20	-0.24	-0.26	-0.03	0.80	1.29	0.40
	(2.40)	(3.27)	(3.70)	(3.91)	(-4.96)	(-4.67)	(-5.90)	(-0.43)
Spain	0.46	0.56	0.55	0.57	-0.20	-0.24	-0.26	-0.03	0.80	1.29	0.40
	(2.40)	(3.27)	(3.70)	(3.91)	(-4.96)	(-4.67)	(-5.90)	(-0.43)
Sweden	0.51	0.56	0.49	0.38	-0.09	-0.07	-0.02	0.24	1.19	1.00	0.18
	(4.78)	(5.36)	(4.76)	(3.29)	(-3.60)	(-1.65)	(-0.41)	(3.44)
Malaysia	0.57	0.62	0.63	0.57	-0.09	-0.12	-0.40	0.18	0.94	1.54	0.63
	(3.84)	(4.51)	(5.47)	(4.16)	(-3.69)	(-4.31)	(-10.15)	(2.60)
Malaysia	0.30	0.40	0.48	0.46	-0.08	-0.04	-0.21	0.10	0.82	1.60	0.35
	(2.83)	(4.37)	(4.62)	(4.66)	(-2.21)	(-1.17)	(-3.87)	(1.46)
Taiwan	0.18	0.17	0.40	0.46	0.03	-0.05	-0.45	-0.14	0.40	1.56	0.54
	(1.61)	(1.53)	(4.29)	(4.29)	(1.88)	(-1.53)	(-9.84)	(-2.07)
Brazil	0.25	0.37	0.60	0.61	-0.09	-0.07	-0.09	-0.02	0.33	0.94	0.04
	(1.37)	(1.95)	(2.51)	(2.42)	(-2.06)	(-1.11)	(-0.98)	(-0.20)
Netherlands	0.37	0.48	0.43	0.31	-0.12	-0.08	-0.12	0.19	0.58	0.56	0.27
	(2.34)	(3.05)	(2.82)	(2.01)	(-2.87)	(-1.72)	(-2.64)	(2.18)
South Africa	0.30	0.33	0.44	0.43	-0.08	-0.09	-0.17	0.12	0.71	1.15	0.16
	(2.48)	(2.74)	(4.32)	(4.13)	(-2.36)	(-2.68)	(-4.80)	(1.48)
Singapore	0.25	0.31	0.43	0.46	-0.09	-0.18	-0.01	0.13	0.50	1.16	0.33
	(1.81)	(2.40)	(3.53)	(3.56)	(-2.95)	(-5.13)	(-0.27)	(2.37)
Mexico	0.25	0.26	0.36	0.26	0.00	-0.05	-0.16	0.15	0.48	0.52	0.11
	(1.79)	(1.72)	(2.64)	(1.73)	(-0.06)	(-0.77)	(-2.83)	(2.00)
Norway	0.43	0.48	0.43	0.38	-0.14	-0.15	-0.10	0.08	0.73	0.70	0.12
	(2.29)	(2.74)	(2.66)	(2.40)	(-3.60)	(-1.96)	(-2.10)	(1.02)
Indonesia	0.17	0.15	0.33	0.33	-0.03	-0.13	-0.03	0.03	0.30	0.59	0.02
	(0.94)	(0.78)	(1.97)	(1.96)	(-0.58)	(-2.13)	(-0.46)	(0.43)
Denmark	0.46	0.55	0.37	0.21	-0.05	-0.11	-0.26	0.26	0.72	0.39	0.27
	(1.86)	(2.34)	(2.02)	(1.18)	(-1.46)	(-1.82)	(-3.55)	(3.74)
Thailand	0.03	0.15	0.26	0.29	-0.16	-0.13	-0.18	-0.05	0.09	0.95	0.33
	(0.30)	(1.47)	(2.67)	(2.71)	(-6.00)	(-3.86)	(-4.71)	(-1.11)
Finland	0.44	0.44	0.43	0.26	0.04	0.02	-0.13	0.25	0.88	0.55	0.12
	(3.14)	(3.18)	(3.35)	(1.80)	(1.01)	(0.33)	(-2.33)	(2.49)
Turkey	0.28	0.31	0.38	0.29	0.00	-0.08	-0.02	0.26	0.56	0.64	0.13
	(2.14)	(2.48)	(3.41)	(2.53)	(-0.14)	(-1.46)	(-0.42)	(2.58)
Chile	0.25	0.36	0.42	0.34	-0.12	0.02	-0.08	0.13	0.61	0.89	0.13
	(2.59)	(4.29)	(4.31)	(2.95)	(-1.90)	(0.30)	(-1.47)	(1.55)
Poland	0.19	0.29	0.33	0.25	-0.12	-0.07	-0.04	0.18	0.34	0.53	0.25
	(1.08)	(1.72)	(2.06)	(1.57)	(-3.23)	(-2.24)	(-0.68)	(2.87)
Colombia	0.24	0.13	0.18	0.15	0.07	-0.05	0.02	0.18	0.22	0.14	0.02
	(0.89)	(0.47)	(0.82)	(0.70)	(0.67)	(-0.32)	(0.15)	(0.86)
Austria	0.15	0.20	0.34	0.29	-0.11	-0.11	-0.14	0.27	0.21	0.49	0.32
	(0.82)	(1.27)	(2.23)	(2.08)	(-2.78)	(-2.13)	(-2.72)	(4.53)
Philippines	0.14	0.27	0.48	0.48	-0.12	-0.11	-0.19	0.00	0.18	0.70	0.10
	(0.66)	(1.37)	(2.35)	(2.34)	(-2.68)	(-1.66)	(-3.13)	(-0.03)
Argentina	-0.02	0.33	0.35	0.25	-0.12	0.05	-0.07	0.33	-0.02	0.25	0.17
	(-0.08)	(1.52)	(1.56)	(1.19)	(-3.35)	(0.80)	(-1.35)	(2.42)
Ireland	-0.46	-0.47	-0.42	-0.49	0.01	-0.07	-0.06	0.28	-0.28	-0.31	0.05
	(-1.01)	(-1.03)	(-1.01)	(-1.19)	(0.09)	(-0.66)	(-0.88)	(2.39)
Greece	0.56	0.50	0.77	0.89	-0.09	-0.07	-0.26	0.14	0.60	1.33	0.46
	(2.35)	(2.40)	(4.20)	(4.51)	(-1.85)	(-1.27)	(-4.87)	(1.87)
Portugal	0.47	0.54	0.40	0.54	-0.20	0.09	0.12	0.33	0.41	0.53	0.20
	(1.53)	(1.98)	(1.45)	(1.85)	(-2.43)	(1.46)	(1.87)	(3.83)
Peru	0.26	0.14	0.42	0.42	0.18	0.03	-0.30	0.00	0.28	0.52	0.17
	(1.07)	(0.69)	(2.13)	(2.13)	(1.51)	(0.34)	(-3.94)	(-0.01)
Czech Republic	0.26	0.34	0.44	0.51	-0.03	0.07	-0.06	0.37	0.25	0.52	0.10
	(0.83)	(1.08)	(1.39)	(1.64)	(-0.40)	(0.81)	(-0.87)	(3.06)
New Zealand	0.24	0.31	0.33	0.35	-0.18	-0.14	0.05	0.21	0.36	0.58	0.14
	(1.42)	(1.68)	(1.80)	(1.89)	(-3.06)	(-3.01)	(1.24)	(2.26)
Pakistan	0.40	0.42	0.64	0.63	-0.04	-0.19	-0.14	0.02	0.57	1.02	0.17
	(1.87)	(2.02)	(3.47)	(3.48)	(-1.46)	(-3.46)	(-1.94)	(0.20)

4.7 Time-varying Return of Quality

I also look at the intertemporal properties to see what they tell us about how quality varies over time. Although the sample data only stretches from 2005 to 2019 it does include very shifting economic periods. The boom time leading up to the financial crisis in 2008 is one environment and the following downturn lasting until 2009 another. And finally, the ten-year bull rally up until 2019. From Figure 4‑14 we see the average cumulative factor returns for the global sample. The market ups and down can be seen on the black line and we also see how quality on average performs very stable during the time sample. Asness et al. describe a “flight to quality”, i.e. when the market goes down investors flock to high quality stocks and drive their returns up. The same phenomenon is proven for the value factor and we see that the HML returns heavily influenced by high returns during the financial crisis. My data does not show an equally strong effect on QMJ, but we do see that the QMJ returns are in fact positive during the financial crisis. From Figure 4‑15 we can see the time series of the price of quality (which we analyzed in section 4.5.2). The chart shows the that the slope coefficient of quality in regressions of price on quality increase by 100% during the financial crisis compared to the pre-crisis values.

The “slow and steady” performance of a long quality, sort junk strategy is also shown in Figure 4‑16. It displays, for the US sample, the cumulative abnormal returns using the 4-factor alpha for the quality sorted difference (H-L) portfolio. We see that through bull and bear markets the investment in high quality stocks yield an almost perfectly linear return when hedging for the other factors. The figure is very much in line with the equivalent figures in Asness et al. [1]. Figure 4‑18 shows the QMJ factor returns for all the countries in the sample to give an indication of the variation.

As a curiosity, I have also included the cumulative 4-factor alpha of the quality sorted portfolio for the Norwegian sample in Figure 4‑17. Here we se a clear shift in abnormal returns after the financial crisis, with quality (H-L) earning huge returns after hedging for other risk factors.

In conclusion, we observe the same time-varying properties of quality as found by Asness et al. QMJ and the quality difference portfolio deliver consistent positive risk-adjusted returns over time and it looks to be robust to varying economic environments.

Figure 4‑14: The chart shows the Global average cumulative excess returns from the factor portfolios

formed each month for the factors MKT (market), HML (Value), QMJ (Quality), MOM (Momentum) and SMB (size).

Figure 4‑15: The time-varying price of quality.

This chart shows the slope coefficients from monthly cross-sectional regressions of price on quality as defined in section 4.5.2. The sample is US stocks.

Figure 4‑16: This chart shows the cumulative 4-factor alpha factor abnormal returns

for the difference portfolio (high-low) sorted on quality. Sample is the US Stock Market.

Figure 4‑17: Abnormal returns (alpha) of the Quality sorted portfolios when adjusted for Fama-French-Carhart risk factors.

Sample is norwegian stocks and the estimates are significant for all portfolios from 6 and above.

Figure 4‑18: Cumulative excess returns of a QMJ portfolio formed every month.

Each line represents one of the 44 countries in the global sample. Ireland is the only loss-making country.

4.8 Algorithmic Trading

In this section I explain how the QMJ factor can be used in modern investment practice. With the rise of computing power and accessible data over the last decades, we have also seen a rapid development in the vaguely defined field of quantitative finance. This involves the use of mathematical models on large datasets of financial and can refer to algorithmic trading methods, data driven research and analysis or other way of applying math to draw conclusions from datasets. The workflow of developing a quantitative investment strategy, shown in Figure 4‑19, can be explained by breaking it into several models [31]. First and foremost, a quantitative investor needs large datasets of primarily financial data. Once the raw data is obtained, it must be cleansed and organized so the models can use it.

The return model, somethings called the alpha model, is the heart of the strategy. This model will build on some investment hypothesis that can be used to predict the relative movements of future returns for the asset class being analyzed. For example, we could hypothesize that the future return of a firm’s stock correlates with how often it is mentioned on Twitter, by the historic stock prices or some other pattern. The return model is then tested on the data and its effectiveness can be analyzed by various statistical measures. In the analysis work we have shown how the QMJ alpha looks to be robust and could form the basis of a suitable return model.

The purpose of the risk model is to enable constructing a portfolio in line with the investors risk profile and to minimize risk of losses. This is done by evaluating the performance of the constructed portfolio against some measure of risk. The traditional measure used by Markowitz was portfolio return variance, but more modern risk models use measures like the Sharpe ratio, exposure to factors (e.g. style and sector) or portfolio drawdown to understand the portfolio risk and set limits to exposure.

The portfolio construction model combines and perform trade-off studies between the return model and the risk model combined with a model to take into account trading cost and constraints like the cost of buying a stock, slippage effects or avoiding illiquid assets. Portfolio construction can be done using for instance mean variance methods, but often the investor will optimize the portfolio construction and execution model by performing back tests. Back testing means that you run a simulation of how your algorithm would have performed using historic data. The portfolio construction model describes the rules for selecting assets and trade them at an acceptable cost and risk level and the execution model simulates the actual trading on historic data.

Using this framework, we could create a trading strategy based on the QMJ factor or include the QMJ factor in an existing strategy to take advantage of the abnormal returns we seem to achieve.

Figure 4‑19: Workflow for quantitative investment, adopted from [31]

5 Conclusion

The goal of this thesis is to examine whether the findings for Asness et al.’s paper “quality minus junk” [1] could be replicated when increasing the dataset from 24 countries to 44. The quality factor is a proxy based on an asset pricing model where the future discounted payoffs is split into separate terms relating to profitability, growth and safety. I provide evidence confirming the two research hypothesis, namely that 1: There is a positive and significant relationship between price and quality, and 2: an abnormal risk-adjusted return can be earned by investing in high-quality stocks and shorting low-quality stocks.

The first finding on the positive relationship between price and quality shows that the model specification based on modern asset pricing has explanatory power on stock prices, but most of the cross-sectional variation in prices is still unexplained. This finding is the case in 40 out of the 44 countries examined for the sample data between 2005 and 2019.

The second finding shows that a factor-mimicking portfolio (QMJ) going long on the highest quality firms and shorting the low-quality stocks earns a significant risk-adjusted return with a Sharpe ratio after hedging for other factor exposures just above 1. The risk-adjusted alpha was positive for 43 out of the 44 countries in the sample.

The third finding of this study is that the abnormal quality returns are consistent across the time period and appears robust to changing economic environments. The price of quality stocks do increase during times of distress, indicating a “flight to quality”, but the risk-adjusted alpha (when hedging for other risk factors) does not fall during the financial crisis.

This thesis confirms the results from Asness et al. using a broader sample of countries, but with a short time horizon. In their paper they conclude the abnormal returns of quality stock are due to mispricing and they are unable to find a risk-based explanation. If anything, quality stocks are less risky than lower-quality stocks as measured by Sharpe ratio. The other avenue to pursue would be preference or behavior-based explanation to why the average investor does not wish to hold quality stocks. I find that quality deliver consistent returns during times of distress as well as in times of boom. It is therefore difficult to argue that investors shy away from these stocks to avoid negative returns when the marginal utility of consumption is high. It has been proposed that investor bias like lottery preference and overconfidence [21] could be an explanation why the demand for high-quality stocks is not higher, but they are difficult to prove or disprove. Asness et al. analysis on analysts’ estimates indicate (if analysts’ expectations are a good proxy for market expectations) that the average investor tends to overestimate junk stocks and underestimate quality stocks.

Recommendations for further research would be to perform backtesting of a trading strategy based on QMJ to test whether the strategy delivers abnormal returns also when controlling for constraints like commissions, constraints on short trading, etc. I would also dig deeper into the price of quality. We found quality to explain very little of the cross-sectional variation in price, but by analyzing the relationship between price and the individual accounting components that make up the quality factor or regression of quality on other variables we might learn more to understand why a theoretically sound valuation model explains so little of cross-sectional variation in prices.

References

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Appendix 1 – Table A-1

Table A-1: Persistence of Quality measure across quality sorted portfolios.

Country	Time	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	H-L	t-stat
Argentina	t	-1.75	-1.13	-0.69	-0.36	-0.08	0.19	0.46	0.71	1.05	1.63	3.37	(177.64)
	t + 3Y	-0.68	-0.47	-0.45	-0.27	-0.11	0.06	0.13	0.13	0.45	0.70	1.38	(14.79)
	t + 10Y	0.08	-0.12	-0.39	-0.38	-0.11	-0.17	-0.19	0.13	0.21	0.33	0.26	(1.27)
Australia	t	-1.74	-1.05	-0.67	-0.37	-0.11	0.12	0.37	0.65	1.02	1.79	3.52	(335.83)
	t + 3Y	-0.43	-0.29	-0.18	-0.13	-0.07	-0.01	0.14	0.29	0.42	0.73	1.15	(53.89)
	t + 10Y	-0.36	-0.17	-0.05	-0.04	-0.01	0.07	0.11	0.18	0.23	0.52	0.88	(29.16)
Austria	t	-1.61	-1.09	-0.76	-0.45	-0.15	0.15	0.45	0.76	1.07	1.67	3.28	(155.02)
	t + 3Y	-0.69	-0.59	-0.27	-0.22	-0.17	0.29	0.10	0.38	0.59	0.55	1.24	(12.90)
	t + 10Y	-0.65	-0.16	0.04	0.04	0.20	0.14	-0.11	0.47	0.16	-0.08	0.60	(5.97)
Brazil	t	-1.66	-0.99	-0.67	-0.43	-0.20	0.04	0.33	0.66	1.10	1.82	3.48	(205.09)
	t + 3Y	-0.76	-0.59	-0.50	-0.34	-0.26	-0.07	0.06	0.30	0.68	1.22	1.98	(39.08)
	t + 10Y	-0.48	-0.44	-0.14	-0.12	-0.23	-0.20	-0.23	-0.01	0.24	0.53	0.99	(8.21)
Canada	t	-1.83	-1.03	-0.63	-0.33	-0.09	0.15	0.39	0.65	1.00	1.72	3.55	(190.69)
	t + 3Y	-0.61	-0.29	-0.16	-0.06	0.00	0.08	0.19	0.31	0.51	0.79	1.40	(23.90)
	t + 10Y	-0.24	-0.05	0.00	-0.01	0.06	0.19	0.27	0.28	0.50	0.54	0.78	(9.26)
Chile	t	-1.58	-0.98	-0.68	-0.43	-0.19	0.04	0.27	0.59	1.05	1.93	3.51	(291.95)
	t + 3Y	-0.71	-0.50	-0.37	-0.24	-0.14	0.00	0.14	0.30	0.56	1.03	1.74	(26.93)
	t + 10Y	-0.18	-0.27	-0.06	-0.13	-0.13	0.09	0.08	0.18	0.20	0.63	0.81	(5.61)
China	t	-1.63	-1.06	-0.73	-0.44	-0.18	0.09	0.37	0.68	1.09	1.81	3.45	(506.64)
	t + 3Y	-0.74	-0.67	-0.52	-0.40	-0.30	-0.16	-0.02	0.15	0.42	0.85	1.59	(57.92)
	t + 10Y	-0.40	-0.39	-0.34	-0.38	-0.27	-0.23	-0.18	-0.22	-0.16	0.20	0.60	(11.61)
Colombia	t	-1.76	-1.01	-0.60	-0.32	-0.09	0.14	0.41	0.68	1.03	1.64	3.40	(261.99)
	t + 3Y	-0.99	-0.50	-0.51	-0.24	-0.19	-0.06	0.17	0.42	0.47	1.03	2.02	(13.21)
	t + 10Y	-0.72	-0.21	-0.22	-0.21	-0.01	-0.45	-0.54	-0.37	-0.14	0.41	1.13	(5.68)
Czech Republic	t	-1.55	-1.02	-0.72	-0.41	-0.13	0.12	0.39	0.70	1.00	1.65	3.19	(78.37)
	t + 3Y	-0.35	-0.17	-0.14	-0.29	-0.08	-0.01	0.37	0.31	0.19	0.28	0.64	(3.19)
	t + 10Y	-1.20	-0.23	0.29	-0.60	0.48	0.65	0.09	0.09	-0.23	-0.06	1.82	(41.56)
Denmark	t	-1.48	-0.96	-0.73	-0.53	-0.31	-0.02	0.31	0.67	1.14	1.92	3.40	(246.93)
	t + 3Y	-0.29	-0.40	-0.50	-0.38	-0.20	-0.18	0.07	0.22	0.41	1.16	1.46	(21.32)
	t + 10Y	-0.06	-0.17	-0.41	-0.42	-0.13	-0.19	0.00	0.11	0.14	0.48	0.54	(8.24)
Finland	t	-1.61	-1.03	-0.71	-0.43	-0.16	0.09	0.35	0.65	1.04	1.83	3.44	(231.98)
	t + 3Y	-0.69	-0.46	-0.34	-0.31	-0.17	-0.06	0.19	0.41	0.54	0.98	1.67	(27.84)
	t + 10Y	-0.43	-0.10	-0.22	-0.21	-0.07	0.02	-0.02	0.36	0.70	0.73	1.17	(12.31)
Germany	t	-1.72	-1.06	-0.70	-0.41	-0.14	0.12	0.40	0.69	1.06	1.76	3.48	(591.68)
	t + 3Y	-0.74	-0.46	-0.33	-0.22	-0.08	0.00	0.17	0.33	0.54	0.94	1.68	(55.67)
	t + 10Y	-0.40	-0.34	-0.20	-0.23	-0.07	0.08	0.13	0.28	0.46	0.68	1.08	(21.31)
Great Britain	t	-1.73	-1.07	-0.68	-0.38	-0.12	0.12	0.38	0.66	1.04	1.78	3.51	(678.87)
	t + 3Y	-0.85	-0.47	-0.26	-0.15	-0.10	0.05	0.16	0.35	0.56	1.03	1.88	(79.38)
	t + 10Y	-0.68	-0.25	-0.13	-0.07	-0.07	0.05	0.12	0.18	0.35	0.59	1.27	(30.70)
Greece	t	-1.63	-1.06	-0.73	-0.43	-0.15	0.11	0.37	0.66	1.04	1.83	3.46	(350.98)
	t + 3Y	-0.81	-0.60	-0.46	-0.31	-0.23	-0.04	0.13	0.40	0.47	1.09	1.90	(34.84)
	t + 10Y	-0.49	-0.50	-0.50	-0.24	-0.05	-0.04	0.02	0.26	0.28	0.67	1.16	(18.73)
Hong Kong	t	-1.64	-1.06	-0.72	-0.44	-0.18	0.08	0.37	0.68	1.10	1.82	3.46	(537.86)
	t + 3Y	-0.68	-0.57	-0.43	-0.35	-0.27	-0.18	-0.09	0.08	0.27	0.53	1.21	(56.55)
	t + 10Y	-0.38	-0.34	-0.33	-0.20	-0.25	-0.34	-0.20	-0.15	0.04	0.08	0.46	(19.61)
Hungary	t	-1.99	-1.73	-1.44	-1.28	-1.17	-1.04	-0.94	-0.85	-0.77	-0.68	1.32	(20.61)
	t + 3Y	0.24	-0.42	-0.34	-0.22	0.02	0.15	-1.14	-0.12	-0.13	-0.17	-0.93	(-4.75)
Indonesia	t	-1.77	-1.07	-0.66	-0.38	-0.12	0.15	0.41	0.69	1.04	1.73	3.49	(666.84)
	t + 3Y	-0.81	-0.68	-0.46	-0.34	-0.27	-0.10	0.01	0.14	0.38	1.05	1.86	(57.31)
	t + 10Y	-0.42	-0.39	-0.18	-0.30	-0.22	-0.03	-0.06	-0.04	0.12	0.59	1.01	(11.19)
Ireland	t	-1.71	-0.98	-0.64	-0.37	-0.13	0.11	0.39	0.66	1.03	1.70	3.40	(117.26)
	t + 3Y	-0.27	-0.22	-0.31	0.02	0.23	-0.02	-0.11	-0.05	0.07	0.33	0.60	(4.03)
	t + 10Y	-0.82	-0.38	-0.24	-0.09	0.20	-0.13	-0.07	0.24	-0.09	0.27	1.46	(8.53)
Japan	t	-1.64	-1.05	-0.71	-0.43	-0.17	0.08	0.35	0.66	1.06	1.85	3.49	(716.21)
	t + 3Y	-0.71	-0.58	-0.45	-0.34	-0.22	-0.09	0.06	0.24	0.49	0.96	1.67	(79.45)
	t + 10Y	-0.58	-0.48	-0.44	-0.35	-0.28	-0.14	0.01	0.10	0.33	0.73	1.31	(56.19)
Malaysia	t	-1.66	-1.02	-0.66	-0.41	-0.18	0.07	0.32	0.65	1.09	1.83	3.50	(442.96)
	t + 3Y	-0.66	-0.41	-0.33	-0.28	-0.20	-0.05	0.11	0.25	0.55	1.05	1.71	(38.23)
	t + 10Y	-0.15	-0.05	-0.11	0.02	-0.07	-0.05	0.21	0.20	0.12	0.56	0.72	(16.92)
Malaysia	t	-1.71	-1.08	-0.71	-0.41	-0.14	0.12	0.40	0.70	1.09	1.74	3.45	(582.26)
	t + 3Y	-0.63	-0.58	-0.48	-0.35	-0.17	-0.10	0.11	0.25	0.49	0.92	1.55	(31.71)
	t + 10Y	-0.26	-0.29	-0.38	-0.23	-0.22	-0.12	0.05	0.14	0.24	0.52	0.78	(40.70)
Mexico	t	-1.59	-1.07	-0.72	-0.45	-0.20	0.06	0.40	0.74	1.10	1.75	3.34	(217.21)
	t + 3Y	-0.72	-0.75	-0.62	-0.33	-0.25	-0.16	0.23	0.34	0.60	1.18	1.90	(29.80)
	t + 10Y	-0.10	-0.33	-0.64	-0.47	-0.23	-0.28	-0.11	0.12	0.28	0.58	0.67	(4.85)
Netherlands	t	-1.70	-1.01	-0.65	-0.39	-0.16	0.06	0.33	0.69	1.10	1.76	3.46	(293.37)
	t + 3Y	-0.55	-0.37	-0.24	-0.11	-0.11	-0.04	0.06	0.23	0.44	0.78	1.33	(12.56)
	t + 10Y	-0.54	0.06	0.27	0.04	-0.05	-0.05	0.27	0.21	0.38	0.11	0.62	(5.76)
New Zealand	t	-1.67	-1.04	-0.66	-0.37	-0.14	0.09	0.33	0.62	1.02	1.83	3.50	(277.97)
	t + 3Y	-0.62	-0.38	-0.37	-0.35	-0.08	0.06	0.04	0.22	0.40	0.85	1.46	(17.71)
	t + 10Y	-0.09	-0.17	-0.45	-0.18	-0.20	0.05	0.10	0.02	0.14	0.58	0.66	(3.97)
Norway	t	-1.72	-1.03	-0.65	-0.37	-0.13	0.09	0.34	0.65	1.04	1.79	3.51	(407.33)
	t + 3Y	-0.32	-0.37	-0.27	-0.15	-0.14	-0.07	0.02	0.22	0.38	0.69	1.01	(17.56)
	t + 10Y	-0.39	0.00	-0.15	-0.29	-0.08	-0.05	-0.21	-0.10	0.26	0.55	0.94	(4.83)
Pakistan	t	-1.71	-1.05	-0.69	-0.40	-0.13	0.11	0.36	0.67	1.09	1.76	3.47	(207.29)
	t + 3Y	-0.77	-0.60	-0.36	-0.34	-0.21	-0.04	0.02	0.25	0.49	0.97	1.74	(19.71)
	t + 10Y	-0.59	-0.54	-0.20	-0.21	-0.14	0.12	-0.04	0.18	0.57	0.65	1.23	(30.93)
Peru	t	-1.57	-1.00	-0.68	-0.44	-0.19	0.04	0.27	0.57	1.08	1.92	3.49	(211.13)
	t + 3Y	-0.57	-0.64	-0.26	-0.27	-0.14	-0.01	0.10	0.23	0.59	1.18	1.76	(33.59)
	t + 10Y	-0.38	-0.38	-0.40	-0.35	-0.27	-0.15	-0.06	-0.01	0.43	0.63	1.00	(5.06)
Philippines	t	-1.59	-1.07	-0.71	-0.42	-0.16	0.08	0.34	0.62	1.03	1.88	3.48	(220.86)
	t + 3Y	-0.84	-0.68	-0.37	-0.23	-0.14	0.05	0.24	0.28	0.52	1.06	1.90	(24.23)
	t + 10Y	-0.56	-0.45	-0.09	-0.18	-0.01	-0.04	0.00	0.37	0.42	0.42	0.98	(13.67)
Poland	t	-1.71	-1.00	-0.65	-0.38	-0.15	0.07	0.33	0.65	1.05	1.81	3.52	(260.77)
	t + 3Y	-0.39	-0.33	-0.32	-0.25	-0.18	-0.14	-0.05	0.05	0.35	0.84	1.23	(32.13)
	t + 10Y	0.05	-0.03	-0.07	-0.13	0.08	0.09	0.06	0.23	0.24	0.52	0.48	(3.85)
Portugal	t	-1.66	-0.97	-0.63	-0.37	-0.14	0.07	0.31	0.61	1.01	1.80	3.46	(164.00)
	t + 3Y	-0.63	-0.35	-0.37	-0.24	0.02	0.04	0.01	0.25	0.33	0.80	1.43	(12.26)
	t + 10Y	-0.32	-0.20	-0.48	-0.02	0.22	0.26	-0.30	0.05	0.17	0.31	0.63	(6.24)
Russia	t	-1.76	-1.01	-0.67	-0.38	-0.11	0.13	0.39	0.68	1.04	1.71	3.47	(243.41)
	t + 3Y	-0.76	-0.69	-0.49	-0.42	-0.17	-0.17	-0.04	0.25	0.28	0.66	1.41	(19.32)
	t + 10Y	-0.15	-0.26	0.00	-0.20	-0.23	0.09	-0.15	0.81	0.32	0.45	0.59	(3.66)
Singapore	t	-1.72	-1.06	-0.69	-0.40	-0.15	0.11	0.39	0.70	1.08	1.75	3.47	(488.51)
	t + 3Y	-0.47	-0.43	-0.42	-0.32	-0.19	-0.06	0.00	0.12	0.34	0.67	1.14	(27.17)
	t + 10Y	-0.29	-0.20	-0.17	-0.08	-0.10	-0.01	0.04	-0.01	0.22	0.24	0.54	(8.69)
South Africa	t	-1.71	-1.06	-0.67	-0.38	-0.12	0.11	0.36	0.65	1.03	1.80	3.51	(422.57)
	t + 3Y	-0.68	-0.57	-0.39	-0.19	-0.10	-0.02	0.15	0.24	0.42	0.82	1.50	(39.46)
	t + 10Y	-0.38	-0.24	-0.25	-0.27	-0.18	-0.07	0.07	0.23	0.28	0.27	0.62	(8.49)
South Korea	t	-1.67	-1.08	-0.73	-0.44	-0.17	0.10	0.39	0.71	1.11	1.77	3.44	(715.74)
	t + 3Y	-0.79	-0.69	-0.59	-0.42	-0.31	-0.20	-0.08	0.14	0.31	0.73	1.52	(26.20)
	t + 10Y	-0.52	-0.47	-0.32	-0.33	-0.36	-0.22	-0.19	-0.01	0.01	0.33	0.86	(47.10)
Spain	t	-1.67	-1.04	-0.69	-0.40	-0.12	0.12	0.35	0.64	1.03	1.81	3.48	(269.31)
	t + 3Y	-0.65	-0.51	-0.38	-0.23	-0.13	-0.03	0.12	0.34	0.60	1.02	1.66	(21.39)
	t + 10Y	-0.49	-0.14	0.13	0.07	-0.12	0.08	0.09	0.46	0.25	0.67	1.16	(12.20)
Spain	t	-1.67	-1.04	-0.69	-0.40	-0.12	0.12	0.35	0.64	1.03	1.81	3.48	(269.31)
	t + 3Y	-0.65	-0.51	-0.38	-0.23	-0.13	-0.03	0.12	0.34	0.60	1.02	1.66	(21.39)
	t + 10Y	-0.49	-0.14	0.13	0.07	-0.12	0.08	0.09	0.46	0.25	0.67	1.16	(12.20)
Sweden	t	-1.68	-1.06	-0.71	-0.40	-0.13	0.12	0.37	0.66	1.03	1.81	3.49	(459.65)
	t + 3Y	-0.41	-0.32	-0.30	-0.22	-0.05	0.06	0.24	0.39	0.59	0.99	1.40	(26.67)
	t + 10Y	0.04	-0.13	-0.09	0.11	0.31	0.30	0.37	0.44	0.39	0.76	0.72	(11.67)
Switzerland	t	-1.56	-1.03	-0.74	-0.47	-0.21	0.06	0.34	0.67	1.09	1.87	3.43	(226.51)
	t + 3Y	-0.76	-0.52	-0.45	-0.20	-0.14	-0.03	0.15	0.36	0.64	1.14	1.90	(30.43)
	t + 10Y	-0.66	-0.51	-0.32	-0.17	-0.09	0.03	0.13	0.34	0.34	0.74	1.40	(20.48)
Switzerland	t	-1.56	-1.03	-0.74	-0.47	-0.21	0.06	0.34	0.67	1.09	1.87	3.43	(226.51)
	t + 3Y	-0.76	-0.52	-0.45	-0.20	-0.14	-0.03	0.15	0.36	0.64	1.14	1.90	(30.43)
	t + 10Y	-0.66	-0.51	-0.32	-0.17	-0.09	0.03	0.13	0.34	0.34	0.74	1.40	(20.48)
Taiwan	t	-1.64	-1.08	-0.73	-0.45	-0.17	0.10	0.39	0.71	1.09	1.79	3.43	(741.48)
	t + 3Y	-0.63	-0.58	-0.48	-0.37	-0.28	-0.07	0.08	0.27	0.50	0.93	1.56	(59.58)
	t + 10Y	-0.32	-0.33	-0.28	-0.35	-0.26	-0.05	-0.03	0.03	0.20	0.40	0.72	(17.31)
Thailand	t	-1.74	-1.06	-0.67	-0.38	-0.14	0.12	0.39	0.69	1.05	1.76	3.50	(557.28)
	t + 3Y	-0.74	-0.61	-0.45	-0.27	-0.22	-0.02	0.06	0.20	0.46	0.92	1.66	(33.17)
	t + 10Y	-0.35	-0.23	-0.21	-0.22	-0.20	-0.20	-0.05	0.09	0.05	0.19	0.53	(6.10)
Turkey	t	-1.71	-1.06	-0.69	-0.42	-0.12	0.15	0.40	0.67	1.05	1.75	3.47	(242.05)
	t + 3Y	-0.81	-0.43	-0.41	-0.29	-0.07	0.09	0.18	0.38	0.57	0.92	1.73	(46.10)
	t + 10Y	-0.29	-0.12	-0.21	0.02	0.00	0.11	0.16	0.29	0.27	0.41	0.70	(11.88)
United States	t	-1.60	-1.01	-0.73	-0.47	-0.21	0.06	0.34	0.67	1.08	1.87	3.47	(313.63)
	t + 3Y	-0.76	-0.62	-0.49	-0.36	-0.20	-0.07	0.10	0.30	0.56	1.01	1.77	(56.42)
	t + 10Y	-0.42	-0.46	-0.43	-0.27	-0.10	-0.05	0.00	0.17	0.30	0.58	1.00	(58.65)

Appendix 2 – Table A-2

Table A-2: Regressions of quality-sorted portfolio excess returns on risk factors

Country		P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	H-L
United States	Excess Return	-1.86	-1.13	-0.88	-0.90	0.33	-0.60	-0.22	-0.39	-0.20	-0.11	1.75
		(-1.73)	(-1.14)	(-0.97)	(-0.99)	(0.26)	(-0.74)	(-0.26)	(-0.50)	(-0.26)	(-0.14)	(3.68)
	CAPM α	-1.18	-0.76	-0.29	-0.32	0.03	-0.07	0.19	0.06	-0.10	0.38	1.55
		(-2.36)	(-1.31)	(-0.69)	(-0.74)	(0.04)	(-0.20)	(0.54)	(0.16)	(-0.36)	(1.45)	(3.34)
	3-factor α	-1.06	-0.25	-0.48	-0.26	-0.48	-0.07	-0.01	0.02	-0.19	0.08	1.14
		(-2.55)	(-0.49)	(-1.13)	(-0.67)	(-0.97)	(-0.24)	(-0.03)	(0.04)	(-0.58)	(0.27)	(3.60)
	4-factor α	-0.95	-0.68	-0.52	0.00	-0.41	-0.07	-0.15	-0.12	-0.31	-0.18	0.77
		(-2.57)	(-1.08)	(-1.37)	(-0.02)	(-0.94)	(-0.22)	(-0.42)	(-0.39)	(-0.91)	(-0.67)	(3.23)
	Sharpe Ratio	-0.63	-0.43	-0.36	-0.37	0.11	-0.27	-0.10	-0.19	-0.10	-0.05	1.96
	Information Ratio	(-1.14)	(-0.75)	(-0.77)	(-0.01)	(-0.55)	(-0.10)	(-0.21)	(-0.16)	(-0.42)	(-0.30)	(1.04)
Great Britain	Excess Return	-0.77	-0.41	-0.22	-0.03	0.05	0.15	0.42	0.58	0.46	0.81	1.58
		(-1.64)	(-0.98)	(-0.50)	(-0.06)	(0.11)	(0.34)	(0.99)	(1.34)	(1.21)	(2.21)	(8.59)
	CAPM α	-1.11	-0.56	-0.58	-0.53	-0.21	-0.31	0.42	0.34	0.23	1.12	2.23
		(-3.77)	(-2.22)	(-1.99)	(-1.68)	(-0.80)	(-1.14)	(1.78)	(1.49)	(0.97)	(4.18)	(8.97)
	3-factor α	-1.04	-0.37	-0.42	-0.47	-0.10	-0.24	0.47	0.34	0.35	1.19	2.23
		(-4.11)	(-1.63)	(-1.60)	(-1.65)	(-0.44)	(-0.81)	(1.73)	(1.33)	(1.43)	(4.57)	(9.18)
	4-factor α	-1.05	-0.52	-0.49	-0.55	-0.18	-0.33	0.47	0.38	0.33	1.17	2.22
		(-4.07)	(-2.25)	(-1.91)	(-1.93)	(-0.72)	(-1.10)	(1.81)	(1.70)	(1.40)	(4.50)	(9.68)
	Sharpe Ratio	-0.55	-0.36	-0.18	-0.02	0.04	0.13	0.37	0.48	0.44	0.79	2.32
	Information Ratio	(-1.25)	(-0.66)	(-0.66)	(-0.69)	(-0.23)	(-0.42)	(0.63)	(0.53)	(0.47)	(1.67)	(2.90)
Japan	Excess Return	0.58	0.68	0.65	0.71	0.61	0.70	0.64	0.80	0.70	0.74	0.16
		(1.15)	(1.49)	(1.43)	(0.00)	(1.26)	(1.46)	(1.33)	(0.00)	(0.00)	(1.38)	(1.24)
	CAPM α	0.14	0.32	0.47	0.40	0.37	0.62	0.45	0.55	0.48	0.73	0.59
		(0.51)	(1.29)	(1.81)	(1.55)	(1.53)	(2.37)	(1.96)	(2.50)	(2.21)	(2.84)	(0.00)
	3-factor α	0.20	0.35	0.52	0.46	0.42	0.64	0.51	0.59	0.61	0.71	0.51
		(0.79)	(1.47)	(2.10)	(1.88)	(1.75)	(2.54)	(2.26)	(2.82)	(2.95)	(3.05)	(2.96)
	4-factor α	-0.06	0.30	0.37	0.35	0.27	0.43	0.39	0.43	0.46	0.63	0.68
		(-0.23)	(1.24)	(1.75)	(1.41)	(1.13)	(1.70)	(1.79)	(1.98)	(2.04)	(2.77)	(3.42)
	Sharpe Ratio	0.38	0.49	0.47	0.50	0.42	0.49	0.44	0.53	0.45	0.45	0.28
	Information Ratio	(-0.08)	(0.43)	(0.61)	(0.53)	(0.40)	(0.65)	(0.59)	(0.64)	(0.68)	(0.95)	(1.08)
Hong Kong	Excess Return	0.96	0.91	0.94	0.79	1.00	0.97	0.90	0.81	0.93	0.87	-0.10
		(1.22)	(1.15)	(1.20)	(1.00)	(1.29)	(1.27)	(1.23)	(1.10)	(1.37)	(1.26)	(-0.38)
	CAPM α	1.23	0.92	0.72	-0.03	0.97	1.80	0.87	0.93	0.74	1.15	-0.08
		(1.68)	(1.88)	(1.45)	(-0.04)	(1.63)	(1.59)	(2.08)	(2.25)	(1.70)	(2.54)	(-0.14)
	3-factor α	0.62	0.68	0.77	0.29	0.71	0.86	0.69	0.79	0.44	0.64	0.02
		(1.85)	(1.68)	(2.08)	(0.58)	(1.83)	(1.93)	(1.81)	(2.25)	(1.21)	(1.39)	(0.06)
	4-factor α	0.60	0.46	0.76	0.66	0.69	0.66	0.72	0.68	0.46	0.49	-0.11
		(1.74)	(1.05)	(1.95)	(1.50)	(1.88)	(1.58)	(1.84)	(1.92)	(1.26)	(1.09)	(-0.25)
	Sharpe Ratio	0.46	0.43	0.47	0.38	0.49	0.47	0.49	0.43	0.52	0.46	-0.11
	Information Ratio	(0.45)	(0.35)	(0.60)	(0.50)	(0.57)	(0.57)	(0.67)	(0.67)	(0.43)	(0.42)	(-0.06)
China	Excess Return	1.54	1.54	1.70	1.74	1.70	1.72	1.68	1.72	1.80	1.90	0.36
		(1.58)	(1.68)	(1.82)	(1.89)	(1.79)	(1.85)	(1.77)	(1.82)	(1.98)	(2.21)	(1.43)
	CAPM α	0.10	-0.09	0.08	0.44	0.39	0.78	0.63	1.46	0.97	1.29	1.20
		(0.22)	(-0.20)	(0.19)	(0.92)	(0.93)	(1.54)	(1.45)	(2.83)	(2.77)	(2.52)	(2.11)
	3-factor α	0.36	-0.10	0.40	0.58	0.97	0.26	0.09	1.27	1.21	0.79	0.43
		(0.76)	(-0.25)	(1.01)	(1.42)	(2.32)	(0.55)	(0.15)	(2.91)	(2.69)	(1.92)	(0.79)
	4-factor α	0.70	-1.81	0.53	0.63	1.04	0.04	-0.93	1.11	2.26	1.34	0.63
		(1.12)	(-1.01)	(1.33)	(1.51)	(2.47)	(0.05)	(-0.70)	(2.54)	(1.70)	(2.05)	(1.31)
	Sharpe Ratio	0.54	0.55	0.62	0.64	0.62	0.64	0.61	0.64	0.68	0.78	0.32
	Information Ratio	(0.28)	(-0.25)	(0.32)	(0.40)	(0.56)	(0.01)	(-0.18)	(0.66)	(0.52)	(0.62)	(0.31)
Canada	Excess Return	2.04	1.79	1.50	1.39	1.37	1.08	1.20	1.30	1.15	1.35	-0.69
		(2.61)	(2.27)	(1.74)	(1.80)	(1.86)	(1.55)	(1.77)	(2.01)	(1.98)	(2.68)	(-1.64)
	CAPM α	1.70	1.69	1.13	1.32	0.95	1.16	1.02	1.14	1.05	1.39	-0.32
		(3.00)	(2.87)	(2.23)	(2.80)	(2.20)	(3.20)	(3.39)	(3.94)	(4.00)	(5.30)	(-0.66)
	3-factor α	0.89	1.06	0.55	1.04	0.68	0.70	0.76	0.82	0.89	1.14	0.26
		(2.07)	(2.97)	(1.42)	(3.25)	(2.06)	(2.29)	(2.46)	(2.59)	(3.31)	(5.06)	(0.67)
	4-factor α	0.84	0.93	0.47	0.85	0.77	0.75	0.84	0.99	0.88	1.14	0.30
		(1.95)	(2.55)	(1.26)	(2.58)	(2.42)	(2.47)	(2.97)	(3.43)	(3.38)	(4.93)	(0.80)
	Sharpe Ratio	1.05	0.90	0.70	0.67	0.68	0.57	0.62	0.73	0.70	0.92	-0.58
	Information Ratio	(0.67)	(0.75)	(0.40)	(0.83)	(0.69)	(0.81)	(0.98)	(1.17)	(1.09)	(1.52)	(0.23)
Germany	Excess Return	-0.11	0.22	0.43	0.80	0.30	0.62	0.75	0.79	0.91	0.96	1.07
		(-0.23)	(0.57)	(1.12)	(2.15)	(0.86)	(1.64)	(2.01)	(2.22)	(2.30)	(3.06)	(3.73)
	CAPM α	-0.50	0.58	0.48	0.82	0.11	0.88	0.90	0.05	0.82	0.72	1.21
		(-0.91)	(1.86)	(1.38)	(2.95)	(0.40)	(2.10)	(4.13)	(0.08)	(2.81)	(3.49)	(2.22)
	3-factor α	0.06	0.44	0.51	0.52	0.54	0.70	1.11	0.57	0.85	1.09	1.02
		(0.18)	(1.79)	(1.88)	(2.31)	(2.10)	(2.81)	(5.82)	(3.00)	(3.27)	(6.05)	(2.71)
	4-factor α	0.22	0.31	0.63	0.54	0.50	0.60	0.99	0.54	0.87	1.09	0.87
		(0.65)	(1.18)	(2.42)	(2.42)	(1.92)	(2.30)	(5.48)	(3.05)	(3.31)	(6.14)	(2.49)
	Sharpe Ratio	-0.07	0.19	0.39	0.77	0.29	0.60	0.74	0.84	0.86	0.98	0.98
	Information Ratio	(0.19)	(0.34)	(0.73)	(0.66)	(0.61)	(0.74)	(1.34)	(0.71)	(1.04)	(1.36)	(0.65)
Australia	Excess Return	0.36	0.82	0.60	0.83	0.62	0.95	0.67	0.84	1.01	0.81	0.45
		(0.67)	(1.29)	(0.90)	(0.90)	(0.91)	(1.59)	(1.20)	(1.53)	(1.93)	(1.72)	(1.93)
	CAPM α	-0.36	0.40	-0.16	0.10	0.52	0.90	0.72	0.74	0.87	0.62	0.99
		(-1.09)	(1.09)	(-0.42)	(0.22)	(1.33)	(2.47)	(2.47)	(2.21)	(2.64)	(1.98)	(2.87)
	3-factor α	-0.63	0.41	-0.49	-0.09	0.35	0.69	0.59	0.78	0.91	0.72	1.34
		(-1.94)	(1.15)	(-1.41)	(-0.22)	(1.01)	(2.27)	(2.05)	(2.47)	(2.73)	(2.34)	(4.17)
	4-factor α	-0.68	0.33	-0.48	-0.07	0.38	0.75	0.53	0.74	0.90	0.65	1.34
		(-2.11)	(0.93)	(-1.41)	(-0.20)	(1.11)	(2.50)	(1.90)	(2.32)	(2.76)	(2.12)	(4.11)
	Sharpe Ratio	0.23	0.48	0.34	0.47	0.35	0.56	0.44	0.57	0.75	0.60	0.57
	Information Ratio	(-0.57)	(0.26)	(-0.39)	(-0.06)	(0.33)	(0.72)	(0.60)	(0.85)	(1.04)	(0.76)	(1.08)
South Korea	Excess Return	0.47	0.93	1.24	1.32	1.22	1.22	1.34	1.41	1.46	1.12	0.65
		(0.86)	(1.74)	(2.37)	(2.50)	(2.42)	(2.44)	(2.64)	(2.75)	(2.93)	(2.34)	(2.18)
	CAPM α	-0.09	-0.07	0.19	0.91	0.75	0.90	0.25	0.88	0.65	1.49	1.58
		(-0.13)	(-0.12)	(0.35)	(2.25)	(1.52)	(1.87)	(0.60)	(2.31)	(1.88)	(3.44)	(2.50)
	3-factor α	-0.07	0.07	0.57	1.19	1.09	1.11	0.08	0.91	0.67	1.33	1.40
		(-0.11)	(0.14)	(1.29)	(3.39)	(2.95)	(3.03)	(0.26)	(2.70)	(2.00)	(3.38)	(2.26)
	4-factor α	-0.27	0.04	0.39	1.03	1.05	1.01	-0.15	0.56	0.52	1.17	1.44
		(-0.51)	(0.08)	(0.92)	(3.70)	(3.68)	(3.22)	(-0.50)	(1.84)	(1.55)	(3.46)	(2.34)
	Sharpe Ratio	0.24	0.51	0.65	0.75	0.68	0.66	0.74	0.78	0.80	0.64	0.73
	Information Ratio	(-0.15)	(0.03)	(0.26)	(0.98)	(0.98)	(0.93)	(-0.12)	(0.52)	(0.40)	(0.98)	(0.77)
Switzerland	Excess Return	-0.03	-0.07	0.17	0.65	0.13	0.48	0.45	0.44	0.60	0.91	0.95
		(-0.09)	(-0.20)	(0.50)	(1.81)	(0.34)	(1.41)	(1.28)	(1.22)	(1.53)	(2.27)	(3.24)
	CAPM α	-0.58	-0.20	0.01	0.20	0.22	0.20	0.10	0.33	0.40	0.51	1.09
		(-1.72)	(-0.73)	(0.06)	(0.86)	(0.66)	(0.87)	(0.40)	(1.06)	(1.49)	(1.91)	(2.81)
	3-factor α	-0.02	0.48	0.48	0.40	0.69	0.41	0.35	0.53	0.54	0.38	0.40
		(-0.06)	(1.87)	(2.26)	(1.65)	(2.46)	(1.70)	(1.21)	(1.56)	(2.02)	(1.54)	(1.13)
	4-factor α	-0.23	0.38	0.31	0.28	0.62	0.62	-0.18	0.36	0.43	0.26	0.50
		(-0.65)	(1.24)	(1.45)	(1.24)	(2.30)	(2.34)	(-0.54)	(1.17)	(1.53)	(1.04)	(1.21)
	Sharpe Ratio	-0.03	-0.07	0.17	0.60	0.11	0.47	0.38	0.39	0.51	0.73	1.02
	Information Ratio	(-0.15)	(0.39)	(0.39)	(0.32)	(0.62)	(0.56)	(-0.14)	(0.30)	(0.43)	(0.20)	(0.27)
Russia	Excess Return	0.89	1.13	1.64	1.36	1.52	1.05	1.50	1.28	1.59	1.39	0.50
		(0.92)	(1.29)	(2.04)	(1.45)	(2.23)	(1.69)	(1.78)	(1.97)	(2.41)	(2.01)	(0.74)
	CAPM α	0.71	0.50	1.21	43.50	1.62	1.33	2.36	1.64	1.09	2.52	1.80
		(0.62)	(0.60)	(1.73)	(1.14)	(2.65)	(2.62)	(2.17)	(2.12)	(1.78)	(1.47)	(0.77)
	3-factor α	-1.20	1.05	1.57	-1.36	30.26	1.03	1.50	3.99	0.87	0.94	2.14
		(-1.47)	(0.77)	(1.90)	(-1.12)	(1.15)	(1.18)	(1.88)	(1.28)	(1.07)	(0.51)	(0.98)
	4-factor α	-1.14	3.50	0.89	-0.39	1.19	-1.21	0.74	1.10	-0.21	-4.25	-3.11
		(-1.07)	(1.33)	(1.76)	(-0.77)	(1.93)	(-0.76)	(1.39)	(1.43)	(-0.23)	(-0.97)	(-0.85)
	Sharpe Ratio	0.37	0.55	0.87	0.63	0.83	0.61	0.76	0.74	0.95	0.79	0.25
	Information Ratio	(-0.30)	(0.36)	(0.36)	(-0.20)	(0.43)	(-0.19)	(0.23)	(0.33)	(-0.04)	(-0.25)	(-0.21)
Spain	Excess Return	-0.72	-0.14	0.41	0.14	0.21	0.46	0.62	0.33	0.73	1.01	1.73
		(-1.32)	(-0.25)	(0.87)	(0.32)	(0.44)	(1.07)	(1.46)	(0.84)	(2.10)	(2.96)	(4.76)
	CAPM α	-1.15	-0.32	0.66	0.12	-0.09	0.60	0.30	0.18	0.09	1.33	2.48
		(-3.04)	(-0.78)	(1.77)	(0.38)	(-0.22)	(1.55)	(0.89)	(0.61)	(0.30)	(4.72)	(5.98)
	3-factor α	-0.38	0.18	0.48	0.28	0.17	0.38	0.33	0.09	0.03	0.65	1.03
		(-0.78)	(0.46)	(1.56)	(0.85)	(0.45)	(1.24)	(1.17)	(0.31)	(0.08)	(1.86)	(1.79)
	4-factor α	-0.37	0.29	0.53	0.11	0.09	0.45	0.20	0.34	0.05	0.39	0.76
		(-0.75)	(0.79)	(1.53)	(0.30)	(0.23)	(1.83)	(0.65)	(1.06)	(0.15)	(1.00)	(1.35)
	Sharpe Ratio	-0.44	-0.08	0.29	0.10	0.14	0.36	0.55	0.29	0.68	0.94	1.56
	Information Ratio	(-0.18)	(0.18)	(0.41)	(0.07)	(0.07)	(0.33)	(0.20)	(0.36)	(0.04)	(0.30)	(0.32)
Sweden	Excess Return	-0.72	0.38	0.24	0.29	0.66	0.74	0.95	1.02	1.10	1.05	1.76
		(-1.42)	(0.66)	(0.43)	(0.57)	(1.47)	(1.84)	(2.17)	(2.44)	(2.60)	(2.58)	(5.45)
	CAPM α	-1.02	1.14	-0.75	-0.47	0.68	0.12	0.59	0.84	0.74	1.09	2.12
		(-1.78)	(1.85)	(-1.35)	(-0.93)	(1.54)	(0.27)	(1.37)	(2.01)	(1.49)	(2.98)	(4.52)
	3-factor α	-0.84	1.02	0.27	0.13	0.58	0.75	1.04	1.22	1.37	1.60	2.44
		(-1.53)	(2.13)	(0.51)	(0.24)	(1.33)	(1.62)	(2.00)	(3.72)	(3.33)	(4.37)	(4.53)
	4-factor α	-1.13	0.84	0.24	0.17	0.49	0.57	0.50	0.84	1.27	1.27	2.40
		(-1.93)	(1.94)	(0.45)	(0.35)	(1.13)	(1.22)	(0.90)	(2.45)	(3.27)	(3.64)	(4.39)
	Sharpe Ratio	-0.41	0.25	0.14	0.21	0.47	0.56	0.72	0.80	0.89	0.83	1.44
	Information Ratio	(-0.56)	(0.54)	(0.13)	(0.10)	(0.31)	(0.34)	(0.30)	(0.61)	(0.92)	(0.88)	(1.23)
Malaysia	Excess Return	0.01	0.42	0.62	0.83	0.69	0.67	0.95	0.84	1.01	0.84	0.83
		(0.03)	(1.00)	(1.45)	(2.10)	(0.00)	(1.66)	(2.39)	(2.08)	(2.69)	(2.31)	(3.96)
	CAPM α	-0.12	0.48	0.84	0.90	0.74	0.98	0.97	0.90	1.22	1.05	1.17
		(-0.34)	(1.19)	(2.91)	(2.53)	(2.31)	(3.14)	(4.02)	(3.28)	(4.51)	(0.00)	(2.76)
	3-factor α	-0.23	0.26	0.97	0.96	0.88	1.13	0.98	1.05	1.25	0.85	1.08
		(-0.63)	(0.89)	(3.26)	(3.26)	(0.00)	(4.23)	(4.29)	(4.19)	(4.99)	(0.00)	(2.49)
	4-factor α	-0.29	0.25	1.04	0.83	0.77	1.06	0.75	0.92	1.09	0.69	0.98
		(-0.82)	(0.87)	(3.54)	(0.00)	(2.34)	(4.07)	(3.19)	(0.00)	(4.46)	(3.08)	(2.27)
	Sharpe Ratio	0.01	0.27	0.42	0.60	0.48	0.50	0.72	0.65	0.81	0.68	1.07
	Information Ratio	(-0.24)	(0.25)	(1.10)	(0.87)	(0.79)	(1.30)	(1.03)	(1.18)	(1.45)	(0.98)	(0.77)
Taiwan	Excess Return	0.36	0.65	0.81	0.92	0.92	0.97	0.92	0.98	0.90	0.95	0.58
		(0.63)	(1.16)	(1.49)	(1.72)	(1.79)	(1.74)	(1.69)	(1.76)	(1.63)	(1.77)	(2.26)
	CAPM α	-0.33	-0.37	-0.01	0.65	0.21	0.70	0.12	0.49	0.71	0.50	0.83
		(-1.16)	(-1.45)	(-0.03)	(1.81)	(0.67)	(1.92)	(0.53)	(1.66)	(2.72)	(1.61)	(2.47)
	3-factor α	-0.40	-0.31	-0.01	0.55	0.15	0.81	0.08	0.48	0.69	0.58	0.98
		(-1.74)	(-1.47)	(-0.05)	(1.81)	(0.58)	(2.44)	(0.35)	(1.87)	(2.79)	(2.05)	(3.28)
	4-factor α	-0.36	-0.29	-0.06	0.50	0.15	0.75	0.02	0.45	0.66	0.70	1.05
		(-1.54)	(-1.41)	(-0.25)	(1.72)	(0.58)	(2.55)	(0.07)	(1.95)	(2.86)	(2.91)	(3.75)
	Sharpe Ratio	0.21	0.38	0.48	0.56	0.56	0.57	0.56	0.58	0.53	0.55	0.59
	Information Ratio	(-0.38)	(-0.37)	(-0.07)	(0.51)	(0.17)	(0.90)	(0.02)	(0.54)	(0.83)	(0.86)	(1.04)
Brazil	Excess Return	0.10	1.37	0.78	1.02	1.49	1.64	1.46	1.04	1.47	1.36	1.26
		(0.17)	(1.91)	(1.21)	(1.71)	(2.36)	(2.56)	(2.46)	(1.78)	(2.61)	(2.69)	(3.87)
	CAPM α	0.75	2.80	0.70	1.68	1.15	2.28	1.13	0.72	1.44	1.24	0.49
		(1.14)	(5.10)	(1.08)	(3.96)	(2.28)	(3.39)	(1.75)	(1.33)	(2.73)	(4.07)	(0.64)
	3-factor α	1.22	2.02	1.67	1.54	1.54	1.21	2.20	0.71	1.49	1.23	0.01
		(2.24)	(3.08)	(1.14)	(3.30)	(2.71)	(1.49)	(3.64)	(1.38)	(3.20)	(2.96)	(0.02)
	4-factor α	1.69	1.65	1.12	1.27	1.27	0.37	1.88	0.55	1.25	0.92	-0.76
		(3.21)	(2.11)	(0.79)	(2.31)	(2.29)	(0.40)	(3.39)	(1.05)	(3.12)	(2.25)	(-1.13)
	Sharpe Ratio	0.05	0.66	0.43	0.58	0.92	0.94	0.88	0.63	1.00	1.02	0.84
	Information Ratio	(0.71)	(0.63)	(0.22)	(0.68)	(0.65)	(0.12)	(1.02)	(0.30)	(0.84)	(0.58)	(-0.24)
Netherlands	Excess Return	-0.70	0.21	0.27	0.45	0.27	0.90	0.64	1.13	0.31	1.08	1.78
		(-1.23)	(0.38)	(0.51)	(0.97)	(0.62)	(2.32)	(1.49)	(2.51)	(0.72)	(2.40)	(4.46)
	CAPM α	-0.84	0.05	0.43	0.83	0.09	1.12	0.59	1.58	1.12	0.37	1.21
		(-1.50)	(0.09)	(0.76)	(1.30)	(0.16)	(2.52)	(1.05)	(2.71)	(2.07)	(0.61)	(1.42)
	3-factor α	-0.40	1.10	1.00	0.99	0.41	0.93	0.44	0.78	1.37	0.08	0.48
		(-0.46)	(1.49)	(1.75)	(1.37)	(0.76)	(1.77)	(0.64)	(1.33)	(2.64)	(0.15)	(0.49)
	4-factor α	-1.17	0.87	0.09	1.81	0.12	1.39	0.20	-0.26	0.83	0.34	0.00
		(-1.13)	(0.94)	(0.15)	(2.23)	(0.22)	(1.72)	(0.26)	(-0.34)	(1.36)	(0.51)	(1.30)
	Sharpe Ratio	-0.37	0.11	0.15	0.27	0.17	0.63	0.44	0.74	0.24	0.81	1.39
	Information Ratio	(-0.27)	(0.22)	(0.03)	(0.68)	(0.06)	(0.49)	(0.07)	(-0.08)	(0.39)	(0.14)	(0.37)
South Africa	Excess Return	0.60	0.64	1.06	0.95	0.76	1.01	0.88	1.19	1.12	1.38	0.78
		(1.20)	(1.76)	(3.03)	(2.62)	(1.94)	(2.79)	(2.52)	(3.59)	(3.27)	(4.32)	(2.04)
	CAPM α	0.32	1.01	1.43	0.94	0.95	0.53	0.99	1.97	0.97	1.52	1.20
		(0.53)	(2.83)	(2.87)	(2.82)	(1.95)	(1.19)	(2.45)	(4.80)	(3.09)	(2.99)	(2.09)
	3-factor α	-0.02	1.25	0.98	0.88	1.22	-0.01	0.76	1.90	1.07	1.18	1.20
		(-0.05)	(3.00)	(2.20)	(2.57)	(2.97)	(-0.01)	(2.07)	(4.33)	(3.50)	(3.09)	(2.59)
	4-factor α	0.00	1.34	1.00	0.77	1.20	0.07	0.86	1.87	0.89	1.17	1.17
		(0.01)	(3.40)	(2.15)	(2.19)	(2.93)	(0.15)	(2.43)	(4.28)	(2.61)	(3.22)	(2.68)
	Sharpe Ratio	0.45	0.54	1.11	0.87	0.66	1.03	0.88	1.22	1.17	1.54	0.63
	Information Ratio	(0.00)	(0.70)	(0.59)	(0.47)	(0.90)	(0.05)	(0.69)	(1.38)	(0.77)	(1.04)	(0.62)
Singapore	Excess Return	0.40	0.58	0.71	0.68	0.61	0.66	0.86	0.87	0.74	0.96	0.56
		(0.57)	(0.78)	(1.13)	(1.09)	(1.00)	(0.96)	(1.44)	(1.46)	(1.33)	(1.67)	(1.52)
	CAPM α	0.46	0.60	1.16	0.86	0.15	0.84	0.77	1.17	0.74	1.41	0.95
		(1.19)	(1.62)	(2.42)	(2.11)	(0.43)	(2.17)	(2.65)	(3.99)	(3.16)	(4.24)	(1.93)
	3-factor α	0.23	1.52	0.91	0.74	0.14	0.87	0.72	1.27	0.65	1.29	1.06
		(0.65)	(1.60)	(2.09)	(2.08)	(0.38)	(2.56)	(2.52)	(3.48)	(2.91)	(4.21)	(2.31)
	4-factor α	0.44	0.66	0.68	0.71	-0.27	0.59	0.74	0.90	0.60	1.08	0.65
		(0.99)	(1.76)	(1.81)	(2.08)	(-0.71)	(1.93)	(2.54)	(2.69)	(2.45)	(3.66)	(1.38)
	Sharpe Ratio	0.18	0.27	0.38	0.37	0.35	0.36	0.51	0.53	0.47	0.59	0.42
	Information Ratio	(0.24)	(0.40)	(0.50)	(0.56)	(-0.18)	(0.50)	(0.62)	(0.83)	(0.56)	(0.97)	(0.32)
Mexico	Excess Return	0.18	0.17	0.37	0.82	0.50	1.07	1.20	0.87	1.00	1.09	0.91
		(0.43)	(0.43)	(0.89)	(2.66)	(1.38)	(3.58)	(3.95)	(2.91)	(3.00)	(0.00)	(2.83)
	CAPM α	0.68	0.30	0.55	0.91	1.01	1.24	0.93	0.76	0.39	0.95	0.27
		(1.34)	(0.91)	(1.67)	(3.56)	(2.63)	(0.00)	(3.34)	(2.44)	(0.94)	(3.28)	(0.47)
	3-factor α	1.38	0.78	0.83	0.80	1.45	1.12	0.78	0.88	0.61	0.74	-0.64
		(2.92)	(2.65)	(0.00)	(3.11)	(3.92)	(0.00)	(2.18)	(2.79)	(2.75)	(2.26)	(-1.11)
	4-factor α	1.29	-0.64	0.31	0.81	1.44	0.95	0.75	0.77	0.44	0.15	-1.14
		(2.27)	(-1.17)	(0.85)	(2.53)	(2.51)	(2.82)	(1.77)	(2.85)	(1.61)	(0.37)	(-1.58)
	Sharpe Ratio	0.14	0.14	0.33	0.87	0.49	1.19	1.41	0.94	0.94	0.99	0.78
	Information Ratio	(0.66)	(-0.35)	(0.21)	(0.57)	(0.97)	(0.78)	(0.66)	(0.61)	(0.39)	(0.11)	(-0.44)
Norway	Excess Return	-0.35	-0.51	0.34	0.25	0.22	0.33	0.70	0.64	0.67	0.92	1.27
		(-0.54)	(-0.83)	(0.58)	(0.46)	(0.41)	(0.72)	(1.34)	(1.46)	(1.48)	(1.89)	(3.38)
	CAPM α	-1.45	-3.84	0.87	0.64	0.57	0.47	0.84	1.17	0.52	1.31	2.76
		(-1.24)	(-1.35)	(1.71)	(1.22)	(1.42)	(1.49)	(2.21)	(2.60)	(0.72)	(3.54)	(2.28)
	3-factor α	-0.36	-0.39	0.90	0.36	1.04	0.77	1.02	0.85	0.96	1.32	1.68
		(-0.59)	(-0.84)	(1.96)	(0.77)	(2.77)	(2.28)	(2.86)	(1.94)	(2.22)	(3.20)	(2.38)
	4-factor α	-0.64	-0.41	0.86	0.19	0.97	0.39	1.00	0.85	0.82	1.25	1.89
		(-1.11)	(-0.81)	(1.71)	(0.42)	(2.64)	(1.04)	(2.45)	(2.00)	(1.82)	(3.42)	(2.87)
	Sharpe Ratio	-0.18	-0.28	0.22	0.16	0.16	0.26	0.48	0.49	0.50	0.72	0.93
	Information Ratio	(-0.26)	(-0.21)	(0.50)	(0.12)	(0.75)	(0.31)	(0.64)	(0.54)	(0.51)	(0.95)	(0.73)
Indonesia	Excess Return	1.03	1.68	1.88	1.61	1.83	1.64	1.38	1.60	1.94	1.82	0.79
		(2.15)	(3.36)	(3.52)	(3.86)	(3.70)	(3.39)	(3.08)	(3.07)	(3.57)	(3.14)	(2.08)
	CAPM α	1.38	1.32	1.14	1.46	2.06	1.61	1.53	1.47	2.81	1.80	0.42
		(2.85)	(2.82)	(3.50)	(4.84)	(4.25)	(4.39)	(4.00)	(3.54)	(3.54)	(4.13)	(0.89)
	3-factor α	1.30	0.95	0.85	0.99	1.75	1.55	1.45	1.19	2.17	1.95	0.64
		(3.35)	(2.46)	(2.46)	(3.21)	(4.39)	(4.01)	(4.17)	(3.03)	(5.13)	(5.49)	(1.42)
	4-factor α	1.17	0.97	0.69	0.98	1.61	1.51	1.37	1.19	2.19	1.80	0.63
		(3.16)	(2.46)	(1.87)	(3.09)	(4.42)	(3.82)	(3.53)	(3.47)	(5.45)	(5.73)	(1.34)
	Sharpe Ratio	0.73	1.18	1.27	1.20	1.22	1.16	0.94	1.11	1.19	1.19	0.67
	Information Ratio	(0.95)	(0.65)	(0.53)	(0.83)	(1.23)	(1.20)	(0.99)	(0.99)	(1.79)	(1.41)	(0.35)
Denmark	Excess Return	-0.64	0.28	-0.10	-0.13	0.19	0.27	0.70	0.58	0.69	0.96	1.61
		(-1.06)	(0.44)	(-0.18)	(-0.23)	(0.35)	(0.60)	(1.46)	(1.13)	(1.55)	(2.08)	(3.97)
	CAPM α	-0.80	0.38	-0.22	-0.14	0.25	0.87	0.65	0.26	0.79	0.85	1.65
		(-1.53)	(0.66)	(-0.42)	(-0.29)	(0.61)	(1.63)	(1.27)	(0.56)	(1.74)	(1.87)	(2.90)
	3-factor α	-0.37	1.38	0.48	-0.01	0.39	0.46	1.23	0.49	1.07	0.51	0.89
		(-0.44)	(2.20)	(1.22)	(-0.02)	(0.79)	(0.78)	(2.72)	(1.09)	(2.88)	(1.06)	(0.92)
	4-factor α	-0.36	1.19	0.77	-0.28	0.35	0.65	0.86	0.31	0.54	0.43	0.79
		(-0.40)	(1.93)	(1.49)	(-0.48)	(0.61)	(1.18)	(1.63)	(0.65)	(1.27)	(0.86)	(0.76)
	Sharpe Ratio	-0.35	0.17	-0.07	-0.10	0.14	0.19	0.54	0.44	0.57	0.74	1.24
	Information Ratio	(-0.12)	(0.51)	(0.36)	(-0.13)	(0.21)	(0.33)	(0.49)	(0.18)	(0.33)	(0.25)	(0.25)
Thailand	Excess Return	0.57	0.76	0.78	0.82	0.93	1.04	1.07	0.90	0.93	1.02	0.45
		(1.28)	(1.55)	(1.69)	(1.85)	(1.88)	(2.25)	(2.18)	(1.98)	(2.21)	(2.38)	(2.13)
	CAPM α	0.30	0.65	0.62	0.29	1.02	0.80	0.99	0.97	0.92	1.03	0.73
		(1.03)	(1.80)	(2.22)	(1.10)	(4.01)	(3.12)	(3.87)	(3.92)	(3.89)	(4.39)	(2.46)
	3-factor α	0.22	0.60	0.83	0.75	1.02	0.83	0.86	1.36	1.26	1.23	1.00
		(0.84)	(2.18)	(2.97)	(2.73)	(4.20)	(3.48)	(3.24)	(5.48)	(4.88)	(5.47)	(2.96)
	4-factor α	0.29	0.58	0.72	0.61	0.87	0.74	0.63	1.24	1.20	1.15	0.85
		(1.06)	(2.05)	(2.45)	(2.17)	(3.61)	(3.37)	(2.51)	(5.12)	(5.05)	(5.38)	(2.67)
	Sharpe Ratio	0.41	0.52	0.56	0.63	0.72	0.84	0.83	0.73	0.80	0.89	0.59
	Information Ratio	(0.32)	(0.61)	(0.75)	(0.66)	(0.94)	(0.91)	(0.78)	(1.48)	(1.67)	(1.59)	(0.82)
Finland	Excess Return	-0.55	0.02	-0.01	0.40	0.77	0.81	0.63	0.95	0.65	0.92	1.47
		(-1.04)	(0.05)	(-0.02)	(0.84)	(1.65)	(1.87)	(1.48)	(2.22)	(1.47)	(2.35)	(3.95)
	CAPM α	-0.72	-1.29	-1.16	-0.75	0.54	0.79	0.69	1.07	-0.97	0.65	1.38
		(-0.85)	(-1.47)	(-1.46)	(-1.38)	(1.11)	(1.34)	(1.77)	(2.20)	(-0.95)	(1.29)	(1.39)
	3-factor α	0.91	-0.07	0.45	0.39	0.87	0.76	1.42	1.08	0.07	1.10	0.19
		(0.93)	(-0.10)	(0.53)	(0.69)	(1.75)	(1.09)	(3.10)	(2.01)	(0.13)	(2.09)	(0.17)
	4-factor α	1.01	0.17	1.05	0.21	1.37	0.46	1.24	1.32	0.23	0.89	-0.12
		(1.05)	(0.24)	(1.33)	(0.32)	(1.73)	(0.54)	(2.24)	(2.11)	(0.34)	(1.69)	(-0.12)
	Sharpe Ratio	-0.31	0.01	-0.01	0.26	0.54	0.60	0.44	0.64	0.44	0.69	1.22
	Information Ratio	(0.27)	(0.06)	(0.40)	(0.09)	(0.66)	(0.19)	(0.62)	(0.64)	(0.11)	(0.42)	(-0.03)
Turkey	Excess Return	0.86	1.08	1.36	1.35	1.46	1.38	1.63	1.51	1.58	1.86	1.00
		(1.40)	(1.68)	(2.25)	(2.30)	(2.60)	(2.11)	(2.58)	(2.46)	(2.52)	(3.23)	(3.04)
	CAPM α	-0.48	0.42	1.63	-1.07	3.85	0.50	0.96	1.63	0.53	2.83	3.31
		(-0.70)	(0.72)	(2.33)	(-0.45)	(2.09)	(0.80)	(1.63)	(2.32)	(0.77)	(2.10)	(2.31)
	3-factor α	-0.14	0.42	2.37	1.45	2.16	0.73	2.04	1.90	0.16	2.73	2.88
		(-0.22)	(0.64)	(3.52)	(2.22)	(3.26)	(1.29)	(3.21)	(2.67)	(0.25)	(2.79)	(2.61)
	4-factor α	0.07	0.46	2.74	0.90	2.42	0.24	1.55	1.78	0.16	1.94	1.87
		(0.11)	(0.62)	(3.39)	(1.30)	(3.50)	(0.38)	(2.49)	(2.62)	(0.24)	(3.13)	(1.96)
	Sharpe Ratio	0.46	0.55	0.72	0.77	0.75	0.70	0.86	0.80	0.86	1.08	0.86
	Information Ratio	(0.03)	(0.17)	(1.16)	(0.43)	(1.13)	(0.09)	(0.66)	(0.68)	(0.07)	(0.96)	(0.58)
Chile	Excess Return	0.49	0.70	0.71	0.69	0.75	0.81	0.77	0.75	0.91	1.22	0.73
		(1.46)	(2.00)	(2.66)	(2.35)	(2.90)	(3.39)	(3.51)	(3.28)	(3.89)	(4.54)	(3.41)
	CAPM α	0.27	0.31	0.49	0.52	0.64	0.69	0.73	0.70	0.92	1.07	0.80
		(1.30)	(1.38)	(2.03)	(2.81)	(3.24)	(3.30)	(3.56)	(4.22)	(5.68)	(3.97)	(2.93)
	3-factor α	0.26	0.25	0.46	0.20	0.83	0.52	0.75	0.89	1.08	1.16	0.90
		(1.35)	(1.08)	(1.85)	(1.21)	(3.42)	(2.02)	(4.52)	(5.55)	(6.73)	(4.89)	(3.21)
	4-factor α	0.38	0.22	0.47	0.06	0.82	0.45	0.64	0.94	1.01	1.15	0.78
		(1.73)	(0.95)	(1.62)	(0.34)	(3.42)	(1.69)	(3.76)	(5.67)	(5.91)	(4.57)	(2.48)
	Sharpe Ratio	0.50	0.74	0.86	0.88	0.97	1.05	1.17	1.06	1.31	1.54	0.83
	Information Ratio	(0.37)	(0.24)	(0.48)	(0.09)	(1.06)	(0.61)	(0.97)	(1.43)	(1.31)	(1.38)	(0.61)
Poland	Excess Return	0.47	0.57	0.74	0.61	0.56	0.88	0.49	0.63	0.82	0.76	0.30
		(0.53)	(0.78)	(1.09)	(0.82)	(0.92)	(1.35)	(0.71)	(0.93)	(1.40)	(1.33)	(0.60)
	CAPM α	-1.09	0.42	0.56	0.55	0.36	0.60	0.73	-0.10	0.87	0.93	2.01
		(-1.50)	(0.66)	(1.27)	(0.90)	(0.78)	(1.29)	(1.35)	(-0.24)	(2.09)	(2.11)	(2.77)
	3-factor α	-0.94	0.85	0.61	0.52	0.20	0.41	1.04	0.50	0.86	0.68	1.61
		(-1.46)	(1.58)	(1.33)	(0.81)	(0.46)	(0.84)	(1.76)	(1.08)	(1.84)	(2.41)	(2.40)
	4-factor α	-1.09	0.86	0.67	-2.19	0.06	0.01	0.70	0.47	0.69	0.41	1.50
		(-1.71)	(1.72)	(1.38)	(-0.79)	(0.11)	(0.01)	(1.14)	(0.88)	(1.61)	(1.30)	(2.22)
	Sharpe Ratio	0.19	0.29	0.40	0.31	0.30	0.51	0.27	0.38	0.50	0.52	0.20
	Information Ratio	(-0.39)	(0.51)	(0.37)	(-0.20)	(0.03)	(0.00)	(0.37)	(0.25)	(0.40)	(0.34)	(0.58)
Colombia	Excess Return	1.45	1.24	1.02	1.02	0.71	0.81	1.09	1.42	1.48	1.48	0.03
		(3.08)	(2.19)	(2.17)	(2.57)	(2.00)	(1.70)	(1.84)	(3.85)	(3.25)	(2.96)	(0.07)
	CAPM α	1.35	0.01	0.30	1.42	0.08	0.30	1.77	3.42	2.00	1.78	0.44
		(1.63)	(0.02)	(0.61)	(1.57)	(0.13)	(0.68)	(2.36)	(1.46)	(3.02)	(3.02)	(0.43)
	3-factor α	-56.24	1.09	0.87	0.78	-7.33	-0.67	0.61	-1.90	4.11	-1.13	55.11
		(-0.98)	(1.01)	(1.37)	(1.54)	(-0.75)	(-0.57)	(0.57)	(-0.63)	(1.66)	(-0.60)	(0.96)
	4-factor α	-3.18	-0.75	0.60	4.02	5.93	9.80	2.37	1.07	4.07	1.15	4.32
		(-0.47)	(-0.37)	(0.36)	(1.29)	(0.94)	(1.45)	(1.54)	(0.62)	(1.62)	(1.70)	(0.62)
	Sharpe Ratio	0.91	0.77	0.68	0.68	0.55	0.52	0.74	1.16	1.01	0.94	0.02
	Information Ratio	(-0.08)	(-0.09)	(0.07)	(0.42)	(0.39)	(0.74)	(0.41)	(0.21)	(0.58)	(0.48)	(0.16)
Austria	Excess Return	0.06	0.41	-0.06	0.56	0.52	0.81	0.68	0.63	1.05	0.35	0.29
		(0.09)	(0.86)	(-0.12)	(1.09)	(0.96)	(1.56)	(1.42)	(1.45)	(2.79)	(0.79)	(0.59)
	CAPM α	-0.24	-0.36	-0.14	1.28	1.08	2.82	0.52	0.58	0.78	0.76	1.00
		(-0.31)	(-0.75)	(-0.28)	(1.31)	(1.70)	(1.17)	(0.99)	(1.05)	(1.99)	(1.29)	(1.25)
	3-factor α	1.83	-0.42	0.17	0.36	1.64	1.38	-0.22	0.06	-0.06	0.28	-1.55
		(1.54)	(-0.97)	(0.22)	(0.47)	(1.56)	(2.24)	(-0.27)	(0.09)	(-0.11)	(0.54)	(-1.29)
	4-factor α	1.05	-4.74	3.20	-1.39	0.30	2.11	1.11	-1.66	0.18	-1.05	-2.10
		(0.94)	(-1.10)	(1.24)	(-1.47)	(1.05)	(2.04)	(1.25)	(-1.76)	(0.17)	(-1.24)	(-1.55)
	Sharpe Ratio	0.03	0.26	-0.04	0.32	0.32	0.49	0.43	0.44	0.74	0.25	0.15
	Information Ratio	(0.28)	(-0.23)	(0.50)	(-0.35)	(0.29)	(0.61)	(0.34)	(-0.33)	(0.05)	(-0.26)	(-0.35)
Philippines	Excess Return	1.29	1.80	1.58	1.46	0.84	1.70	1.76	1.76	1.39	1.74	0.45
		(2.04)	(3.19)	(3.04)	(2.91)	(1.39)	(3.07)	(3.06)	(3.18)	(3.27)	(3.32)	(1.02)
	CAPM α	1.04	1.72	1.94	1.21	0.31	1.83	4.18	1.22	2.10	1.67	0.63
		(2.07)	(2.97)	(3.50)	(2.02)	(0.57)	(3.15)	(2.01)	(2.11)	(4.44)	(3.98)	(0.96)
	3-factor α	0.37	1.45	1.74	1.27	-0.33	1.83	1.90	1.50	1.94	1.56	1.19
		(1.01)	(2.81)	(3.55)	(2.24)	(-0.41)	(2.85)	(3.31)	(3.09)	(3.91)	(3.72)	(2.20)
	4-factor α	0.33	1.55	1.64	1.79	0.00	1.66	1.81	1.40	2.00	1.56	1.22
		(0.99)	(2.77)	(3.11)	(2.25)	(0.01)	(2.53)	(2.88)	(2.73)	(4.04)	(3.32)	(2.15)
	Sharpe Ratio	0.70	1.06	1.06	0.95	0.49	1.09	1.11	1.15	1.07	1.28	0.27
	Information Ratio	(0.21)	(0.76)	(0.80)	(0.66)	(0.00)	(0.71)	(0.91)	(0.72)	(1.23)	(0.87)	(0.54)
Argentina	Excess Return	1.92	1.82	2.49	1.79	2.67	2.69	2.68	2.51	1.87	2.33	0.40
		(2.27)	(2.49)	(3.20)	(2.34)	(3.40)	(3.76)	(3.52)	(4.08)	(2.95)	(4.03)	(0.68)
	CAPM α	-0.24	-0.78	0.24	1.95	1.94	1.14	3.73	1.92	1.95	1.79	2.03
		(-0.19)	(-0.71)	(0.24)	(2.39)	(1.96)	(1.56)	(3.93)	(1.86)	(2.42)	(2.33)	(1.29)
	3-factor α	0.06	-1.71	-0.62	1.45	2.52	0.76	5.44	2.08	4.94	1.57	1.52
		(0.03)	(-1.38)	(-0.46)	(1.19)	(1.42)	(0.89)	(3.98)	(1.40)	(1.96)	(1.65)	(0.63)
	4-factor α	-0.33	-1.08	0.15	3.67	3.43	1.09	5.31	3.55	0.94	2.71	3.05
		(-0.17)	(-0.76)	(0.10)	(2.35)	(1.70)	(0.99)	(3.72)	(1.98)	(0.60)	(2.14)	(1.14)
	Sharpe Ratio	0.71	0.80	1.13	0.81	1.27	1.42	1.32	1.27	0.98	1.33	0.17
	Information Ratio	(-0.05)	(-0.20)	(0.03)	(0.86)	(0.57)	(0.29)	(1.44)	(0.80)	(0.16)	(0.73)	(0.42)
Ireland	Excess Return	0.46	1.49	0.97	-0.19	0.03	-0.34	0.34	-0.55	-0.06	0.75	0.28
		(0.54)	(1.71)	(1.32)	(-0.19)	(0.03)	(-0.34)	(0.40)	(-0.78)	(-0.07)	(1.06)	(0.34)
	CAPM α	2.17	14.90	3.14	2.91	0.37	0.00	-1.31	-3.55	8.18	-0.33	-2.50
		(0.92)	(1.08)	(1.25)	(1.45)	(0.30)	(1.12)	(-0.31)	(-2.05)	(1.07)	(-0.24)	(-0.88)
	3-factor α	2.22	4.98	1.95	20.17	4.16	-1.36	17.18	-0.76	3.94	10.02	7.80
		(0.58)	(2.28)	(0.50)	(1.13)	(0.63)	(-0.26)	(1.33)	(-0.35)	(0.69)	(1.49)	(1.04)
	4-factor α	-0.33	1.24	-0.47	3.40	1.28	1.56	-10.30	-0.36	-1.05	-5.25	-4.91
		(-0.17)	(1.02)	(-0.27)	(1.90)	(0.70)	(0.00)	(-0.95)	(-0.30)	(-0.59)	(-0.98)	(-0.88)
	Sharpe Ratio	0.16	0.54	0.40	-0.06	0.01	-0.11	0.13	-0.22	-0.02	0.35	0.09
	Information Ratio	(-0.04)	(0.25)	(-0.06)	(0.61)	(0.15)	(0.34)	(-0.13)	(-0.06)	(-0.15)	(-0.22)	(-0.20)
Greece	Excess Return	-0.33	0.54	0.02	0.38	0.22	0.12	0.44	0.65	0.42	0.60	0.92
		(-0.45)	(0.88)	(0.03)	(0.57)	(0.33)	(0.19)	(0.64)	(1.21)	(0.81)	(1.13)	(2.32)
	CAPM α	-0.23	0.49	-0.27	0.80	0.22	0.28	0.88	0.78	0.52	0.40	0.62
		(-0.33)	(0.80)	(-0.50)	(1.19)	(0.36)	(0.51)	(1.73)	(2.08)	(1.23)	(1.05)	(0.96)
	3-factor α	0.10	-0.92	0.22	0.44	-0.20	0.14	1.23	0.23	0.24	0.50	0.40
		(0.13)	(-1.19)	(0.33)	(0.62)	(-0.41)	(0.31)	(2.54)	(0.60)	(0.58)	(1.42)	(0.45)
	4-factor α	0.16	-0.70	0.66	0.66	-0.48	0.06	0.92	-0.01	0.07	0.34	0.18
		(0.18)	(-1.07)	(0.89)	(0.90)	(-0.87)	(0.12)	(1.64)	(-0.02)	(0.18)	(1.00)	(0.19)
	Sharpe Ratio	-0.14	0.26	0.01	0.17	0.10	0.06	0.22	0.41	0.26	0.38	0.55
	Information Ratio	(0.04)	(-0.22)	(0.25)	(0.25)	(-0.17)	(0.03)	(0.46)	(-0.00)	(0.04)	(0.25)	(0.05)
Portugal	Excess Return	0.40	-0.09	0.35	1.07	0.11	0.78	1.53	0.76	0.61	1.40	1.00
		(0.57)	(-0.13)	(0.62)	(1.32)	(0.19)	(1.16)	(2.46)	(1.44)	(1.30)	(2.46)	(1.43)
	CAPM α	1.69	-0.42	0.36	1.59	0.16	1.45	1.02	0.86	0.39	2.60	0.91
		(1.30)	(-0.40)	(0.35)	(1.49)	(0.17)	(1.25)	(1.05)	(0.92)	(0.38)	(2.93)	(0.66)
	3-factor α	1.04	-9.34	-0.64	2.98	-0.49	12.82	3.40	22.08	6.13	0.58	-0.46
		(0.68)	(-1.27)	(-0.34)	(0.91)	(-0.07)	(1.48)	(0.61)	(0.91)	(1.42)	(0.30)	(-0.17)
	4-factor α	-1.05	0.08	46.63	-87.03	15.06	-16.29	0.13	-13.50	85.62	4.45	5.51
		(-0.62)	(0.00)	(1.26)	(-1.53)	(1.18)	(-1.27)	(0.01)	(-1.36)	(0.86)	(0.41)	(0.47)
	Sharpe Ratio	0.15	-0.04	0.17	0.42	0.06	0.37	0.74	0.42	0.34	0.63	0.33
	Information Ratio	(-0.15)	(0.00)	(3.24)	(-0.04)	(0.74)	(-0.13)	(0.00)	(-0.24)	(37.06)	(0.10)	(0.13)
Peru	Excess Return	1.44	1.35	1.33	1.59	1.84	1.96	1.39	1.63	1.88	1.84	0.40
		(2.85)	(2.67)	(2.54)	(3.69)	(4.28)	(3.54)	(2.49)	(4.45)	(4.48)	(2.51)	(0.58)
	CAPM α	0.52	1.46	1.75	1.68	1.64	1.48	1.38	1.65	1.50	2.16	1.64
		(1.49)	(3.09)	(2.49)	(4.60)	(3.55)	(2.81)	(3.23)	(4.13)	(4.20)	(4.80)	(3.19)
	3-factor α	0.32	1.05	0.64	0.95	1.44	1.08	1.11	1.27	0.79	2.26	1.94
		(0.64)	(2.18)	(1.69)	(1.83)	(2.34)	(3.39)	(2.69)	(2.93)	(1.43)	(5.18)	(3.34)
	4-factor α	0.13	0.88	0.45	0.95	1.22	0.90	0.98	1.15	0.70	2.55	2.42
		(0.24)	(1.85)	(1.16)	(2.01)	(2.28)	(2.71)	(2.56)	(2.52)	(1.21)	(4.17)	(3.54)
	Sharpe Ratio	0.93	0.95	0.93	1.35	1.32	1.43	1.06	1.25	1.44	0.95	0.18
	Information Ratio	(0.06)	(0.50)	(0.29)	(0.58)	(0.62)	(0.59)	(0.61)	(0.68)	(0.41)	(0.75)	(0.68)
Czech Republic	Excess Return	1.09	-0.88	0.93	0.54	0.91	0.59	0.57	1.38	1.06	1.01	-0.08
		(1.84)	(-1.72)	(1.71)	(1.05)	(2.96)	(1.63)	(1.32)	(3.37)	(1.86)	(1.80)	(-0.10)
	CAPM α	-0.19	-20.14	42.77	-81.77	57.81	-19.06	-80.13	12.42	13.36	2.36	2.55
		(-0.19)	(-0.58)	(0.99)	(-0.78)	(1.34)	(-0.57)	(-0.86)	(0.85)	(0.15)	(2.30)	(1.84)
	3-factor α	0.34	-0.15	0.94	0.97	-2.35	1.05	0.46	-0.01	0.77	2.57	2.23
		(0.54)	(-0.25)	(2.14)	(1.97)	(-1.03)	(1.85)	(1.53)	(-0.02)	(1.04)	(2.74)	(1.81)
	4-factor α	0.43	-0.15	0.67	1.07	0.30	0.61	0.39	0.37	0.78	1.97	1.53
		(1.01)	(-0.50)	(1.75)	(2.46)	(0.75)	(1.55)	(1.40)	(0.96)	(1.28)	(2.78)	(1.72)
	Sharpe Ratio	0.53	-0.38	0.42	0.21	0.62	0.42	0.26	0.92	0.55	0.60	-0.03
	Information Ratio	(0.30)	(-0.11)	(0.50)	(0.66)	(0.17)	(0.42)	(0.36)	(0.24)	(0.40)	(0.77)	(0.51)
New Zealand	Excess Return	0.67	0.44	0.26	0.29	0.68	0.77	0.49	0.67	0.72	1.36	0.69
		(1.20)	(1.13)	(0.71)	(0.76)	(1.88)	(2.07)	(1.33)	(1.96)	(1.96)	(4.34)	(1.26)
	CAPM α	0.74	0.80	-0.29	1.14	0.84	0.72	0.44	0.65	0.19	1.48	0.74
		(1.05)	(1.29)	(-0.42)	(2.59)	(1.60)	(1.03)	(0.55)	(1.08)	(0.34)	(2.84)	(0.87)
	3-factor α	-0.28	0.40	-0.35	0.58	0.28	0.80	0.94	1.31	0.23	2.65	2.93
		(-0.36)	(0.65)	(-0.70)	(0.72)	(0.63)	(1.26)	(1.59)	(1.77)	(0.42)	(3.67)	(2.68)
	4-factor α	-0.14	-0.19	-0.21	0.91	0.30	0.80	0.57	0.62	0.14	1.74	1.88
		(-0.17)	(-0.30)	(-0.31)	(1.66)	(0.62)	(1.45)	(1.04)	(0.98)	(0.26)	(3.25)	(1.83)
	Sharpe Ratio	0.37	0.30	0.19	0.21	0.58	0.57	0.37	0.60	0.70	1.33	0.37
	Information Ratio	(-0.04)	(-0.06)	(-0.08)	(0.40)	(0.13)	(0.40)	(0.26)	(0.25)	(0.07)	(0.90)	(0.54)
Pakistan	Excess Return	1.22	1.11	1.50	1.02	1.61	1.49	1.54	1.64	1.88	1.46	0.24
		(1.63)	(1.60)	(2.40)	(1.51)	(2.32)	(2.04)	(2.13)	(2.49)	(2.93)	(2.36)	(0.46)
	CAPM α	1.90	1.03	1.87	1.67	1.59	1.31	2.63	1.80	2.77	1.78	-0.12
		(2.68)	(1.79)	(2.91)	(2.79)	(2.23)	(2.25)	(3.40)	(3.41)	(4.22)	(3.58)	(-0.19)
	3-factor α	2.04	0.84	1.94	1.55	1.97	0.39	2.95	0.75	2.63	1.29	-0.75
		(2.60)	(1.40)	(3.37)	(2.88)	(2.58)	(0.71)	(3.42)	(1.32)	(3.80)	(2.71)	(-0.89)
	4-factor α	2.13	0.56	1.49	1.17	1.64	0.70	3.49	0.22	2.65	0.90	-1.23
		(2.24)	(0.99)	(2.34)	(2.10)	(2.38)	(0.99)	(3.17)	(0.33)	(4.14)	(1.84)	(-1.17)
	Sharpe Ratio	0.55	0.56	0.82	0.54	0.82	0.81	0.80	0.88	1.10	0.86	0.14
	Information Ratio	(0.71)	(0.25)	(0.73)	(0.52)	(0.68)	(0.28)	(1.42)	(0.10)	(1.26)	(0.49)	(-0.28)

Appendix 3 – Python notebook with code used to perform analysis